Individual and Social Preferences

1. Introduction

Rational choice theory might be considered as the main theoretical model in social sciences. To present this theory, it might be useful to start from a strictly philosophical question: how can we explain the action of a human being? According to John Dupre (2001), the majority of philosophers answered this question by generally saying that to explain an action, it is necessary to establish its purpose and identify the belief or series of beliefs that connect the action to that specific purpose. Thus, if the question were “why did Mary buy those Microsoft stocks?” then the answer could be “because she was looking for a personal gain, and she was sure that the price of Microsoft stocks would have increased.”

Consequently, when an explanation has to take into account a wish or a belief, the action becomes more understandable by portraying it as a rational choice. The rational choice theory, therefore, adds to a model of explanation based on wishes and beliefs the idea that, starting from the same level of certainty, the agents act always in the best possible way for them.

As it is well known, rational choice theory was initially the dominant paradigm in economics. A fundamental premise of neoclassical economics was, indeed, that economic phenomena were essentially the product of the actions of fully rational, equal, and, therefore, indistinguishable agents, who were individually and exclusively pursuing their own personal agenda. A premise of a more epistemological nature supported this idea by emphasizing that economic phenomena could be described by some general laws expressed in mathematical terms, exactly as in the case of physics. Therefore, by trying to develop economics as mathematical economics, neoclassical economics aimed at finding a function that might play the same role of energy in physics, that is, a function that could identify maximum and minimum thresholds to define equilibrium states. This comparative criterion was found in the concept of utility, which was introduced in 1789 by Jeremy Bentham as a response to the problem of the justification of ethics. According to Bentham’s definition, a fair choice is a choice that provides the most positive consequences, seen as the difference in terms of happiness between an action and its consequences. Utility was then reinterpreted by neoclassical economics to express it as a mathematical function.

According to the dominant interpretation of utility in neoclassical theory, a rational choice consists in acting to maximize personal utility, or in other words, choosing the option that provides the highest level of satisfaction to the agent. In other words, choosing the greatest gain or the lesser evil is what determines the action.

Undoubtedly, over the past two decades, this explanatory model has exercised a considerable influence beyond the sphere of economics. The implementation of rational choice theory to social sciences was initially due to its universal aspiration. By supporting the idea that all individuals followed the same pattern of reasoning, shared the same intentions, and had a rationality that manifested itself in the same way at all times, all social phenomena became explainable by using the same model. Furthermore, the purely mathematical nature of the model allowed simultaneously to construct an individual process of deliberation and to describe analytically different social phenomena.

Nevertheless, over the years, rational choice theory and the utility function of agents have been widely criticized, aiming, in particular, at the problems concerning the descriptive capacity of these concepts, because in the real world, many individual decisions often do not abide by the perfect logic proposed by the two theories.

In this sense, the strongest criticism came from the representatives of the so-called cognitive-behavioral research in the field of experimental economics. Starting from the pioneering works of Herbert Simon (1955, 1956, 1957, 1972) and the research of cognitive psychologists Kahneman and Tversky (1979, 1984), this discipline frequently highlighted that real agents make choices in a way that is systematically different compared with the models proposed by rational choice theory, thus emphasizing its limits. The goal of behavioral economics became therefore to understand how real agents make decisions and to “describe” the psychological patterns and mechanisms that may lead to a specific choice.

Therefore, while rational choice theory focused primarily on normative and prescriptive issues, behavioral economics took an interest in the descriptive aspects of decision making. This allowed to shed some light on the contradictions existing in the assumptions followed by standard economic models, including the groundless concept of “utility function” that assigned to every action a value specifying its desirability level. In fact, the research carried out in this field identified a series of strong discrepancies that went well beyond utility theory and that caused, for example, an overconfidence in judgment or a complete upsetting of the preferences and biases, a fact that demonstrated a systematic breach of logic and a violation of probability theory by the agents involved. The introduction of psychological variables—such as motivation, emotions, or representation systems independent of the conscious mind and therefore mostly unconscious—strongly questioned the Homo Oeconomicus model, which had enjoyed great success in analyzing both individual decisions and even more complex decisions, like those entailing interactions among different decision makers and typical of game theory. More specifically, by intensifying their studies and putting their ingenuity to the test with new experiments, psychologists lent support to the idea that individual preferences might not only be guided by self-interest but that they could also be not directly self-interested: as a matter of fact, there is a series of social preferences that can be positively or negatively affected by the behavior, preferences, and intentions of other individuals.

Thanks to numerous experiments, behavioral economics outlined two useful concepts that found a strong place in this new theoretical landscape: the concepts of fairness and reciprocity. The former corresponds to the desire for equity, and it translates a kind of individual sensitivity into what can be called “spontaneous justice (or injustice).” The latter describes instead the symmetrical relationship between two agents based on the experimentally proven premise that Homo Oeconomicus does not act only to satisfy his own material interest (as proposed by standard theory) but that he often looks beyond his own interest and takes into account also the interests of other members of his own group because he believes that when the other members of his group will make a choice, they will symmetrically consider his interest.

However, rather than considering standard normative theory as ill-equipped to explain some of the results obtained by behavioral economists, different economists and to a lesser extent some epistemologists in social sciences attempted to include within normative theory the results of several experiments and empirical observations that showed all the dimensions of a choice made by an individual. Consequently, they developed a series of theories to rationalize some of the experimental results that challenged the predictions of standard theory. In this sense, some authors have been advocating for a new approach that is not intended as a challenge to standard theory but rather as its psychological extension, in other words, an approach that could combine normative rules with human motivations, which are considered determinants of economic behavior and, therefore, elements that can enrich the standard definition of a function of maximizing and selfish utility. In these models, new determinants of behavior are linked to deep psychological mechanisms and to the way in which individuals assess the environment that surrounds them, in other words to, their perception of the social interrelation networks characterizing the context in which they take a decision. Accordingly, these models try to establish a less “parsimonious” utility function that could account for different experimental evidence without having to find a specific utility function for every economic change or environment. The objective is, therefore, to find, even in this case, a single utility function that could provide satisfactory predictions according to the existing assumptions and restrictions.

It is possible to identify two different approaches in these models. The first approach is called “distribution-based” approach, and it refers to the theory of individual decisions; the second one is called “psychological game theory” (or “context-based” approach), ¹ and it refers to game theory. Due to this fact, the second approach may be regarded as a generalization of the first one, because the properties of preference relation depend on the general context, which includes also the behavior of the agents surrounding the decision maker.

The second and third section of this article critically analyze the advantages and limitations of these new models that do not aim at challenging the alleged rationality of the agents but rather provide a more homogeneous definition of their preferences and, therefore, of the utility functions that represent them. Yet, despite all these models share the merit of focusing an increasing amount of attention on the choices made by economic agents by considering their beliefs and preferences and, therefore, by turning them into an important principle and an explanation for their decisions, they cannot always completely account for the behavior at an individual level or as equilibria produced by the combination of all the actions of a set of players. Starting from these preliminary considerations, we will demonstrate in section 4 how the ideas of the economist Michael Bacharach—who regarded the knowledge of agents and their problem-solving skills as key elements—can provide a better description of the complexity in the behavior of the agents (and of their society) compared with what standard game theory or the more recent psychological game theory can do.

2. Distribution-Based Models

As previously stated, many academics have already highlighted that rational choice theory has wrongly integrated the maximization program according to the model of selfish preference. In particular, behavioral economics experts question the sometimes surrealistic hypothesis that rationality—intended as exclusive pursue of personal interest—always leads to the description of economic agents as individuals who have, on one hand, substantial mental skills that make them perfectly able to memorize, analyze, and process all data at their disposal, while, on the other hand, these substantial computational capabilities are exclusively used to make always the same choice, which is the one that maximizes their personal utility. In doing so, this approach could not account for important variables like trust, loyalty, and reputation, which even though do not naturally exclude the idea of a rational argument, at the same time, they do not postulate it either (Sen 1977).

To escape the limitations and implausibility of this assumption, one solution could be to redefine individual preferences to include not only what an individual considers to be his or her personal social role but also the roles of the other individuals with whom he or she coordinates to form his or her society. As a matter of fact, it is unclear why rationality does not include the rational pursuit of all objectives and individual values rather than limiting itself exclusively to selfish objectives, which represent only one class of objectives (Schianchi 1997).

Yet, if the assumption that individual preferences evolve as a result of repeated social interactions is true, then it becomes necessary to move away from an analysis based on a strictly individual level and head toward an analysis based on a relational level in which individual aspirations are profoundly affected by social conventions, customs, ideals, and feelings toward others. As a matter of fact, the self-interest model is useful to explain how individuals make self-interested decisions that obviously affect their behavior, but at the same time, it fails to highlight the fact that these self-interested decisions are only factors that guide the behavior of individuals. Therefore, by going beyond the usual requirements of microeconomic rationality intended as a methodological device built mainly on the alleged greediness and selfishness of individuals, several economic scholars have highlighted the need for a new approach that could include human motivations (in particular, different forms of altruism, sense of fairness, or aversion to inequality) in the list of determinants of economic behavior (which, in this case, is excessively short), hence updating the usual definition of utility function.

To explain these forms of behavior, researchers proposed the so-called distribution-based theories, which replace material payoff with a function of social utility. In these theories, preferences are considered interdependent elements and utility depends on the payoff of others. A classic example is provided by the models that postulate an aversion-to-inequity scenario in which agents are ready to sacrifice resources to increase the material payoff of the others if their payoff is lower than an estimated “fair” level, or to decrease their payoff if it is considered higher than an estimated “fair” level.

From this point of view, Fehr and Schmidt (1999) carried out one of the first studies that tried to provide a model of selfless behavior and therefore account for even the most complex motivations. In their model, agents are considered individuals averse to inequity (understood in general terms and not as shown by other agents); consequently, they give importance only to the altruistic nature of their gain, without considering the altruism of their opponents. In this way, the authors emphasize that aversion to inequity may justify cooperation in specific circumstances and non-cooperation in others. At the same time, it is the presence of agents averse to inequity among players that determines the final result. In the model outlined by the two authors, the aversion to inequity by the players formally translates into the following utility function:

U i ( x ) = x i − α i 1 n − 1 ∑ j ≠ i m a x { x j − x i , 0 } − β i 1 n − 1 ∑ j ≠ i m a x { x i − x j , 0 } ,

where n represents the number of players, α i 1 n − 1 ∑ j ≠ i m a x { x j − x i , 0 } measures the loss of utility by player i when his or her gain x _i is lower thanthe gain of j (gain equivalent to x _j ), and β i 1 n − 1 ∑ j ≠ i m a x { x i − x j , 0 } is theconsecutive loss due to a gain by player j; ɑ _i ≥ β _i , describes instead the loss of utility by player i in the event in which his or her gain is lower than the gain of j.

Fehr and Schmidt consider this method a better tool than standard economic theory to explain and justify the abnormal behavior of certain games (especially the Ultimatum Game). ² However, in the context of games in which the goal is to prevail on the competition, it is clear that altruism cannot be the prevailing strategy. As a matter of fact, altruism spurs cooperation only in specific conditions, for example, in asymmetric games, ³ where the propensity to cooperate is lower. Besides, Fehr and Schmidt admit the existence of an even more substantial limitation to their model, highlighting that it does not take into account the analysis of the players’ strategies that sometimes tend to equilibrium ⁴ (in fact, the propensity to altruism of some players cannot explain the tendency toward equilibrium). For this reason, scholars like Binmore and Shaked (in Kirman and Teschl 2010) noticed that the explanatory scope of Fehr and Schmidt’s model is limited because it justifies only few specific situations. ⁵

Bolton and Ockenfels (2000) proposed their “distribution-based” model in their ERC theory (equity, reciprocity, and competition theory). In this model, the utility function is conceived as a “function of motivation”:

v i = v i ( y i , σ i ) ,

σ i = σ i ( y i , c , n ) = { y i / c if c > 0 1 / n if c = 0 ,

and

c = ∑ j = 1 n y i ,

where n represents the number of players, y _i the gain of player i, y _j the gain of player j (j = i), and c is the sum of the players’ gains with the exception of i; σ _i represents instead the consideration of the sum of the players’ gains in function of the motivation of i.

The function v _i reflects the fact that players are motivated to make choices by the gains that they can achieve in the game and their relative gains, or in other words, the gains that they can achieve compared with the total sum of the gains of the other players involved in the game. Therefore, the model postulates a utility function that corresponds to a “mediation” between self-interest (corresponding to the highest possible material gain) and the gains of other players. Consequently, the function of motivation increases in function of personal gain and relative gain. However, from this model, it is clear that a player would prefer to have more than less for himself or herself compared with relative equivalent amounts (Bolton and Ockenfels 2000, 171). Yet, this model is limited by the fact that agents are heterogeneous because nobody can “mediate” in the same way between selfishness and sharing. Therefore, the influence of this “comparison effect” in the utility function is different for every agent.

Another model in which preferences are presented using the value of parameters that define a utility function is the model proposed by Charness and Rabin (2002). Contrary to the first two models, Charness and Rabin’s model considers primarily the search of social welfare. Formally, in a two-player game, the utility function corresponds to the weighted sum of the monetary gain of one player and of the other player. The consideration given by the first player to the gain of the second player depends on how much higher (or lower) this gain is compared with his or her gain and on how big this gap is. Therefore, the propensity of an individual to sacrifice a part of his or her material gain depends on the importance given to this gap, which is formally defined by the following formula:

U B ( π A , π B ) ≡ ( ρ ⋅ r + σ ⋅ s + θ ⋅ q ) ⋅ π A + ( 1 − ρ ⋅ r − σ ⋅ s − θ ⋅ q ) ⋅ π B ,

where

r = 1 if π_B > π_A, and r = 0 otherwise;

s = 1 if π_B < π_A, and s = 0 otherwise;

q = −1 if A has misbehaved, and q = 0 otherwise.

The parameters ρ and σ refer to the gains, while θ is related to reciprocity, and r and s indicate the importance given by the agent to the gains of other players compared with his or her own gain. The formalization of some values of the “distributional preferences” parameters (r, s, q) accounts for the selfish forms of behavior characterizing players who prefer gaining as much as possible at the expenses of others, but these parameters account also for the aversion to inequity. Consequently, this model is designed to highlight that players are not indifferent to the distribution of gains of other players. Social preferences show that individuals are inclined to sacrifice a part of their personal gain to help those in need. Contrary to the ideas of Bolton and Ockenfels, then, it is not the average gain of other players that guides behavior but the distribution of these gains. Considering the results obtained in their experiments, these authors suggest that what explains at best this kind of behavior is a psychological tendency that promotes reciprocity among players. According to Charness and Rabin, reciprocal forms of behavior play, indeed, a stronger role than non-reciprocal forms of behavior, and they must be combined with preferences aiming at promoting social welfare. In this way, players tend to sacrifice a part of their gain because of the supposed and predictable behavior of other players. For example, a player will tend to sacrifice a part of his or her gain to punish someone who misbehaves while, on the other hand, he or she will tend to make sacrifices to increase the gain of a player manifesting a “good disposition.” Nevertheless, in this model, negative reciprocity plays a more dominant role compared with positive reciprocity (the more the players feel that another player will misbehave, the more they want to punish him or her). Finally, despite Charness and Rabin’s model did not take into account the heterogeneity of players and, therefore, had a clear limitation that was even highlighted by the authors themselves, by emphasizing the role of reciprocity, this model represented a relevant step forward on the way leading to a stronger awareness of the social or collective forms of rationality, paving the way for the second type of models presented in this article: the approaches proposed by psychological game theory, also called “context-based” models.

3. Psychological Game Theory

Psychological game theory was initially developed by Geanakoplos who, together with some colleagues, started a generalization process of non-cooperative traditional game theory in which utilities were defined on the beliefs concerning the agents’ actions (Geanakoplos, Pearce, and Stacchetti 1989). In psychological game theory, utility functions are defined in a wider domain than in traditional non-cooperative game theory, and utility maximization requires always some sort of “mediation” between a monetary gain and a secondary gain that is psychologically defined. In this model, gains ultimately depend on the beliefs that agents formulate considering the strategies chosen by other agents. Therefore, the gains are not only material but also psychological, and they are all considered in the matrix of gains, while their importance depends on the hierarchies of the agents’ beliefs. This leads to a classification of beliefs based on “what the player thinks of what the other thinks and what he thinks the other might think that other people think . . . Ad infinitum” (Geanakoplos, Pearce, and Stacchetti 1989, 61).

As in the framework of standard game theory, also in psychological game theory, players find themselves in a situation of common knowledge that promotes equilibrium. This unique profile of strategy generates a set of beliefs in all players and at all levels. Assuming the existence of such an alignment of beliefs is extremely important to solve the game because in the framework of psychological game theory beliefs are endogenous and do not correspond to a predetermined ex ante distribution. As a matter of fact, equilibrium is defined as a psychological Nash equilibrium in which players suppose that beliefs conform to a reality shared by all and that all players will comply to that reality: “Everybody, assuming that you all will comply . . . Ad infinitum” (Geanakoplos, Pearce, and Stacchetti 1989, 65). In other words, the Nash psychological equilibrium represents a strategy that maximizes the utility of an agent x, considering the strategy of other players and the beliefs of x. Therefore, there is only one difference from the standard version of Nash equilibrium: the fact that in this case players’ beliefs are taken into account. However, what is clear from the model of Geanakoplos is that the final results depend equally on the beliefs and on the strategy choices taken by others. In a number of cases, psychological games do not consequently solve the usual problems of indeterminacy. In fact, preferences are related to beliefs, and therefore the troublesome indeterminacy of beliefs is at the basis of the inaccuracies in the model (Hargreaves and Varoufakis 2004). Indeed, considering the fact that beliefs affect gains, they must be known beforehand, yet it seems that this need is never met, because the model requires beliefs that are not ranked according to a predetermined distribution criterion and that are verifiable only during the game.

To overcome these difficulties, Dufwenberg and Kirchsteiger (2004) proposed a more general model that combined the revision of beliefs by an agent, the beliefs of other agents, and the other agents’ action plan. Considering this issue, the two scholars wrote,

However, to handle this problem turns out to be more complicated than in usual game theory. As play unravels in a sequential game, a player who revises his beliefs may also have to revise his beliefs about what type other players are, because kindness depends on beliefs. Therefore, the way in which the player is affected by reciprocity concerns may differ dramatically between different parts of the game tree. (Dufwenberg and Kirchsteiger 2004, 271)

At the same time, they considered also that

Intuitively, a strategy is inefficient if there exists another strategy which, conditional on any history of play and subsequent choices by the others, provides no lower material payoff for any player, and a higher material payoff for some player for some history of play and subsequent choices by the others. (Dufwenberg and Kirchsteiger 2004, 276)

This revision provides the two authors with the opportunity of including a series of dynamic psychological effects that were not included in the previous models. This model, which can be applied extensively to games, allows the analyis of situations that involve strategic interactions. Furthermore, the introduction of sequentiality requires taking into account a dynamic element: the individual is motivated by his or her beliefs at every level of the game. In addition to this, the perception of the kindness of an action depends also on the options that an individual has at his or her disposal.

Therefore, considering all these elements, a utility function is described with the following formula:

u i : Z × ∏ j ∈ N M j × ∏ j ∈ N S j → ℜ

where Z represents the set of terminal nodes, N is the set of players, M _j is the set of conditional beliefs of j about the strategies of other players and of their conditional beliefs, while S _j is the set of pure strategies of j. The strategies and beliefs are considered conditional elements to the progress of the game, while the players’ utility depends on their strategies as well as their higher order beliefs about their respective strategies.

However, the model described above assumes that individuals have full responsibility of the final results, while the monitoring processes of the choices or decisions taken previously by an individual may affect his or her decision-making process, thereby reducing the range of possible actions. Consequently, the degree of responsibility of the individual in the choices made may be altered, and it may lead to a desire for reward or punishment. ⁶

However, what is truly important in Dufwenberg and Kirchsteiger’s model is the fact that it highlighted that all reciprocal acts require an analysis of the intentions underlying the actions taken. The first part of their model defines the generosity of individuals. Contrary to previous models of reciprocity, kindness is measured as an aversion to inequality, or in other words, in function of the gain obtained by others. Introducing the concept of reciprocity in economic reasoning allows for a better understanding of the emergence of cooperative mechanisms among individuals, which leads human beings to consider others and their well-being in their maximization program. The strength of reciprocity preferences takes into account the heterogeneity of individual choices, overcoming in this way the limitations of previous models. This final feature of Dufwenberg and Kirchsteiger’s model is what makes it the most used and successful model in academic literature, even though—similarly to previous models—it is highly complicated to implement because of its multiple (and sometimes counterintuitive) equilibria that are due to the high number of strategic situations postulated by psychological game theory.

To sum up, all models presented above share the merit of justifying certain forms of behavior like cooperation, coordination, and reciprocity, as well as some forms of “deviant” behavior (such as those recorded in the Ultimatum Game or in the Prisoner’s Dilemma ⁷ ). All these models highlight that, in certain circumstances, it is extremely important to consider the context of reference and that all agents are not equal. Undoubtedly, the latter aspect represents a step forward compared with standard game theory in which agents are completely independent of their environment and they perform their maximizing estimations in complete isolation, without any consideration for the others. Nevertheless, even though according to Fehr and Schmidt “no other deviations from the standard economic approach are necessary to account for the evidence” (Fehr and Schmidt 1999, 818-19), it is a strong limitation that the results produced by these models are highly dependent on the values that are obtained from the parameters of the different models considered above. Indeed, the models presented in the previous sections keep many ideas of standard theory in which the self-interest of agents is a key element: agents consider other players only because doing so is in their personal interest and, consequently, they almost never develop a project or an activity that is actually shared with other agents. Furthermore, these models are not suited to justify all possible deviations. In most cases, they just consider the types of behavior emerging in games like “Prisoner’s Dilemma” or “Ultimatum Games,” analyzing only in very few cases what happens in non-simultaneous games. Therefore, although these models outline the hypothesis of interdependent preferences, the concepts concerning the nature of strategic interaction and the rationality of individual are not substantially different from what is proposed in standard game theory. The only new elements introduced refer, therefore, to utility functions. In some of these models, preferences are still exogenous and predefined, exactly as in the standard version of economic applications of game theory.

4. Bacharach’s Approach

As previously stated, the main limitation of the models presented so far lies in their incapacity to clearly determine the role played by beliefs, which are at the basis of the decisions made by agents. This fact proves that it is insufficient to build fairness models based simply on interdependent preferences and developed only on a material point of view, while it is essential to determine in the most precise possible way the role played by intentions and beliefs (Hargreaves and Varoufakis 2004).

Besides, there is an even more serious problem that needs to be considered; game theory (both in its standard and psychological version) aims at becoming a social theory and, therefore, its goal is not only to describe the behavior of single individuals but rather the behavior of the society formed by individuals. The models mentioned so far provide an “answer” to this issue by postulating that society is the product of the interaction among the individuals that compose it and that only individuals have intentions. In this way, the authors do not exclude the possibility of assigning non-intentional forms of behavior to individuals or characterizing them by such behavior, focusing instead on avoiding attributing intentions to entities that are not individuals. Then, they reduce the scope of intentionality by stating that “Every agent maximizes [its] own satisfaction, taking into account the constraints imposed by its environment.” (Schianchi 1997, 126) Therefore, in all models previously described, the behavior of an agent is intentional if its representation describes the purpose of the agent, the means that the agent might use, and the relation existing between the purpose and the means. At the same time, although the label intentional refers to the form of representation, or in other words, if the representation may or may not explain the purpose and means of the agent, the label rational is used to describe the agent only in the case that such judgment is issued by a theoretician about a representation that may correspond (or not) to the behavior that he or she would have had if he or she had been in the same situation of the agent. Ultimately, the label rational refers to the nature of the discourse of the theoretician: he or she must comply with the rules of logic to process the representation of an agent’s behavior, which in its turn may be considered by the theoretician as a behavior that corresponds to the interpretation that he or she would have had if he or she had been in the same situation as the agent. Subsequently, this label might be “transferred” also to the actual behavior of the agent in the case that the actual behavior of the agent endorses the representation made by the theoretician.

This happens because the waiting process for the equilibrium and the structure of the game are the most important elements of these models, while interdependent preferences are considered less important. On the contrary, it often seems that preferences depend more on the way in which the game is played rather than on the matrix of the game. Therefore, it is the perception of the game by the player that guides his or her choice, not a predefined system of preferences established by a theoretician. As a matter of fact, it is important to remember that reason and intentionality are not related a priori. A theoretician, for example, may provide an intentional representation that clarifies the purpose and means of an agent, but this does not mean that the theoretician understands the agent or that he or she is trying to establish how sensible the agent’s behavior is. Or, in another case, a theoretician might support a representation that clarifies the purpose and means of an agent without even considering the task of understanding the behavior of the agent.

Starting from these considerations, the economist Michael Bacharach (2001) can be considered as the most successful author among those who attempted to overcome the problems discussed so far. Bacharach’s approach is interesting, because it provides a possible answer to all the questions and limitations highlighted in the models presented in the previous sections. First of all, it is important to underline that Bacharach developed a model in which subjective representations of the world coexist until they converge toward a unique representation that creates a common group interest, thereby promoting a particular articulation of individual and collective forms of rationality. In his theory, Bacharach makes a clear distinction between the rationality of the agent and the rationality of the observer (or the modeler). As already mentioned, this distinction is particularly relevant because it allows us to understand individual and collective forms of rationality without having to refer only to the analytical methods and the point of view of game theoreticians but by referring to the perception of the agent. This is why it is so important for Bacharach to distinguish between the formal representation of the game by theoreticians and the representation made by the agents. As highlighted in this article, this distinction is not made either in standard or in psychological game theory, and the actual forms of behavior exhibited by the agents are considered to be identical to the representation provided by the theoretician. On the contrary, according to Bacharach, “The answers to fundamental questions about coordination and cooperation . . . lie in the agent’s conception not of the objects of choice, nor of the consequences, but of herself and of the agents with whom she is interacting” (Bacharach, Gold, and Sugden 2006, 70).

Unlike previous models, with his proposal Bacharach tries to answer the question of how agents “team reason,” ⁸ or in other words, how they adopt an attitude aiming at answering the question “what should we do?” (in this regard, it is worthwhile mentioning that in previous models the starting question was always “what should I do?”). To face the question “What should we do?” agents must reason in a valid and functional way to meet their conscious objectives by considering also their subjective beliefs. Rationality is, therefore, measured in terms of consistency between the conclusions drawn from specific premises, but these premises are only available to the agent, and they are not those described and formulated by the modeler.

At the basis of the development of Bacharach’s theory, it is possible to find the concept of “framing,” the process followed by agents to create their representations of the world. “Frames” are mental states or concepts that agents use to make their choices. In the words of Bacharach: “A frame is a set of concepts or predicates an agent uses in thinking about the world” (Bacharach 2001, 1). Therefore, a frame can be defined as a set of concepts that an agent uses to tackle a decision problem because

her frame stands to her thoughts as a set of axes does to a graph; it circumscribes the thoughts that are logically possible for her (not ever but at the time). In a decision problem, everything is up for framing . . . also up for framing are her coplayers, and herself. (Bacharach, Gold, and Sugden 2006, 69)

Therefore, in Bacharach’s theory, group identification is considered as the result of the application of a frame that determines choices based on a change in the logic used to reason to decide what individuals should do. Basically then, “Somebody team reasons if she works out the best feasible combination of actions for all the members of her team, then does her part in it” (Bacharach, Gold, and Sugden 2006, 121). ⁹

The formalization of this approach based on the concept of “framing” is provided by what Bacharach calls “variable frame theory” (VFT). VFT attempts to model the representations made by agents about a problem and about the context in which they must reason. Consequently, VFT retains an objective character in identifying the structure of gains and the set of strategies used by players, but at the same time, it helps in identifying also the subjective side of each player. In general, the decision problem faced by a player is modeled starting from his or her subjective strategies, which are limited by the structure of the game and all his or her representations. According to Bacharach, an agent can “think” using a “We frame” or an “I frame,” and it is precisely starting from these representations that he or she takes his or her decision. If the agent applies a “We frame,” then he or she will tend to cooperate; while in the opposite case, the agent will tend to follow the instinct of maximizing his or her personal gain. Consequently, there are specific circumstances in which an agent thinks in terms of “we,” while in others, he or she thinks in terms of “I.”

Starting from these considerations, Bacharach identifies a series of games that share properties and features that promote group identification, characteristics like interdependence ¹⁰ or the presence of common goals. ¹¹ What makes interdependence and common interest so important is the fact that they create a state of Pareto optimality ¹² in which the higher the gain is, the more convenient it is for the agent to group-identify. In some games, therefore, “team reasoning” represents the best possible strategy, because it allows reaching a state of Pareto optimality, and hence it is logical for individuals to adopt it.

To provide an example of this new way of considering the rationality of players, Bacharach analyzes games similar to Hi-Lo. In general, in these games, every player chooses an element (letter, number) from a common, limited set of options without consulting the other players. Every element is associated with a reward and the peculiarity is that one option is associated to a reward that has a value exponentially higher than the value of all other options. If the players choose the same option, then they will all receive the reward, but if this does not happen, they will not receive the reward. The payoff matrix of Hi-Lo games is described in the following table, which presents the situation of a Hi-Lo game with two players (players 1 and 2), two options (A and B), and their respective rewards (5 and 1).

OPEN IN VIEWER

	Player 1
Player 2	A	B
A	5, 5	0, 0
B	0, 0	1, 1

Bacharach was particularly interested in understanding why all players normally choose the option A, and the answer he found had strong implications—as he admitted—for game theory and on the conception of economic agents (all of us) as social beings. In his own words,

you are to play Hi-Lo, and it is common knowledge that you and your coplayer are intelligent people. It seems quite obvious that you should choose A. However, the question why it seems obvious, and the related question of why people almost always do choose A, have turned out to be anything but easy to answer. (Bacharach, Gold, and Sugden 2006, 35)

The fundamental concept of standard game theory, Nash equilibrium, offers two types of solution for games with a Hi-Lo matrix: the choice (A, A) or the choice (B, B). Considering Nash equilibrium, both solutions are logically possible in correlation with different beliefs, expectations, and ideas of the players. In reality, considering the amounts at stake, one of the two choices is rationally preferable to the other. According to Bacharach, the paradox of Hi-Lo games is due to the “clash” between the rationality of one agent to choose A and the inability of game theory to consider this choice as rational ¹³ .

Therefore, according to Bacharach, the only available possibility left is to consider what he calls “agency transformation,” which requires agents to think about the situation not in terms of an individual decision problem but in terms of a group decision problem. Bacharach supports the idea that group identification tends to produce specific forms of behavior and estimations and that causes a fortiori the appearance of “team reasoning,” which reflects the transition from an individualistic form of reasoning to a form of reasoning that is more oriented to the common good. In other words, “team reasoning” triggers a change in the representations of an individual, who will tend to group-identify and consider himself or herself as part of the group, while at the same time the group will inevitably affect his or her behavior. ¹⁴ This means that the players involved in a Hi-Lo game will not pursue their own personal interest, but they will instead pursue a group utility function that will manifest itself through these steps:

Consequently, in Bacharach’s theory, group identification does not mean only to endorse a specific way of reasoning but also to recognize and to apply it. As Gold and Sugden suggest,

In the theory of team reasoning, an individual who reasons in the “We” frame is aware of the “I” frame too (as one of that other players might use) but acknowledges only “we” reasons. It seems that group identification involves something more than framing in the sense of variable frame theory: the group-identifier does not merely become aware of group concepts, she also becomes committed to the priority of group concepts over individual ones. (Bacharach, Gold, and Sugden 2006, 199)

The players involved in “we” are, therefore, “partners,” agents who cooperate to reach a common objective and who are pursuing a “collective action.” This means that the necessary condition for collective actions is having agents with an equal role (in the sense that they are all agents with the same title in the collective action) ¹⁵ and that their intentions converge toward the same object or common content, which is their shared purpose. ¹⁶

Consequently, to label an action as “collective,” the agents involved in “We” must necessarily be “partners,” or in other words, agents who cooperate to reach the objective of their intention ¹⁷ and their collective action. Finally, for an agent, group-identifying to reach a common goal means to renounce a part (more or less relevant) of his or her own personal objective, while at the same time, it leads also to the creation (or strengthening) of group identity and collective understanding that allows, in any case, to reach higher objectives in less time and more easily.

5. Conclusion

In conclusion, it is possible to state that—despite using the same objective view characterizing also previous studies—Bacharach’s approach is one of the few that does not forget the subjective dimension of the decision-making process by proposing a useful division between the rationality of the agents and the rationality of the observer (or the modeler). Besides its strong explanatory potential, Bacharach’s model distinguishes itself also in terms of its logical foundations. Standard theory and the other theories that took into account altruism and aversion to inequity can be regarded as models of forward-looking behavior in which the intentions of players are irrelevant and the focus is exclusively placed on the distributional aspects relating to the consequences of the choices. On the contrary, Bacharach presents a backward-looking model of behavior in which not only the final distributions of payoff but also the players’ intentions have a motivating effect on the choices. This shows that real agents can successfully coordinate their actions on the basis of contextual information, which often is considered irrelevant from a theoretical point of view. From an experimental point of view, Bacharach’s model introduces an element of realism by considering the effects of social context (social framing effects), which promote the selection of a unique equilibrium by helping in coordinating the players’ expectations. Obviously, this does not mean that Bacharach’s approach is exempt from criticism or limitations. For example, it is unclear how, by conceptualizing “team reasoning” through framing, Bacharach suggests that it is not possible for a player to apply both the “I” frame and “We” frame. In doing so, the author rejects the idea that a player may analyze a decision-making situation in terms of both his own interest and the interest of the group, thus making it difficult to understand the likelihood of defection and conflict of interest related to the structure of some games. ¹⁸ Furthermore, Bacharach’s approach does not consider certain factors that may be important when postulating the existence of a collective or social form of rationality, such as the possible role played by the concept of “social acceptance” (i.e., the importance given to moral norms or social rules, the respect of laws, traditions, customs, etc.) or the “group size” (i.e., the importance that a small group with limited shared knowledge can have compared with a large group where common knowledge is more extensive and where interactions tend to be anonymous). Furthermore, it does not even consider the role played by free riding players, whose personal interest is always in conflict with the group interest.

Nevertheless, Bacharach’s model differs from previous models in one key aspect: Bacharach is one of the few academics who strives to consider not only the formal question of economic relations but also the need of highlighting that in interpersonal economic relations it is always necessary to know what agents think or, in general, what kind of subjective characteristics they have.

In this way, Bacharach succeeded in focusing the attention of researchers on the types of behavior that are at the core of actions in the social world: collective acts and actions that—by taking place on a shared level—are of a higher order and cannot be reduced to the behavior of individual agents.