Team reasoning without a hive mind

The theory of team reasoning has been developed to resolve a long-lasting niggle in orthodox game theory. Despite its intuitive appeal, the theory has received little attention from mainstream game theorists and economists to date. We believe that this is so because of two theoretic issues, which the theory of team reasoning itself needs to resolve. One of these presents a worry that the theory achieves its explanatory and predictive success by abandoning ontological individualism — a fundamental precept in mainstream economics, including game theory. Here we argue that the theory of team reasoning is compatible with ontological individualism. We show that the core principles of the theory — those that give rise to the above worry — are in fact implicitly assumed in some branches of orthodox game theory itself. We also argue against the methodological approach that construes team reasoning as involving a transformation of the interacting players’ payoffs in modelled games.     

The importance of higher-order beliefs to successful coordination

Beliefs about other players’ strategies are crucial in determining outcomes for coordination games. If players are to coordinate on an efficient equilibrium, they must believe that others will coordinate with them. In many settings there is uncertainty about beliefs as well as strategies. Do people consider these “higher-order” beliefs (beliefs about beliefs) when making coordination decisions? I design a modified stag hunt experiment that allows me to identify how these higher-order beliefs and uncertainty about higher-order beliefs matter for coordination. Players prefer to invest especially when they believe that others are “optimistic” that they will invest; but knowledge that others think them unlikely to invest does not cause players to behave differently than when they do not know what their partners think about them. Thus resolving uncertainty about beliefs can result in marked efficiency gains.     

Social connectedness improves co-ordination on individually costly,efficient outcomes

We study the impact of social ties on behavior in two types of asymmetric coordination games. Social ties are varied by making players interact with partners from different in-groups (fellow members of their own sports team, members of their sports club, students of their university). Subjective social ties are further measured by direct questionnaires. We find that smaller and more salient in-groups lead to significantly more group beneficial choices. The same effect is observed for players that report high values of their subjective social ties. We discuss the implication of these results for theories assuming that socially tied individuals follow some group beneficial reasoning.     

Group membership,team preferences,and expectations

Group membership is a powerful determinant of social behaviour in a variety of experimental games. Its effect may be channelled primarily via the beliefs of group members, or directly change their social preferences. We report an experiment with a prisoner's dilemma with multiple actions, in which we manipulate players’ beliefs and show that group identity has a consistent positive effect on cooperation only when there is common knowledge of group affiliation. We also test the robustness of the minimal group effect using three different manipulations: one manipulation fails to induce group identity, and we observe an unsystematic effect of group membership when knowledge of affiliation is asymmetric.     

Conservative belief and rationality

Playersʼ beliefs may be incompatible, in the sense that player i can assign probability 1 to an event E to which player j assigns probability 0. One way to block incompatibility is to assume a common prior. We consider here a different approach: we require playersʼ beliefs to be conservative, in the sense that all players must ascribe the actual world positive probability. We show that common conservative belief of rationality (CCBR) characterizes strategies in the support of a subjective correlated equilibrium where all playersʼ beliefs have common support. We also define a notion of strong rationalizability, and show that it is characterized by CCBR.     

Out of your mind: Eliciting individual reasoning in one shot games

We experimentally investigate the fundamental element of the level-k model of reasoning, the level-0 actions and beliefs. We use data from a novel experimental design that allows us to obtain incentivised written accounts of individuals' reasoning. In particular, these accounts allow to infer level-0 beliefs. Level-0 beliefs are not significantly different from 50, and almost 60% of higher level players start their reasoning from a level-0 belief of exactly 50. We also estimate that around one third of the participants play non-strategically. The non-strategic level-0 actions are not uniformly distributed.     

Resolving Indeterminacy in Coordination Games: A New Approach Applied to a Pay-as-you-go Pension Scheme

This paper shows that when players ignore what outcome will emerge because of the presence of multiple equilibria, they can coordinate their expectations by forming an initial belief based on the principle of indifference followed by a process of reasoning that updates this belief. Since this procedure describes a natural way to form beliefs under indeterminacy, it is reasonable for every agent to conjecture that all the others form their beliefs according to the same logic. Exactly the fact that agents are aware that they form their beliefs following the same procedure allows them to successfully coordinate their expectations.      

Mutual advantage, conventions and team reasoning

This paper proposes a conception of mutual advantage as a motivation for cooperative behaviour. This motivation is contrasted with the ‘emotional’ reciprocity that is represented in current theories of social preferences. The paper explores parallels between mutual advantage and Humean analyses of convention and between mutual advantage and theories of team reasoning.     

创业团队异质性真能促进团队创造力提升吗——一个有中介的调节模型

随着团队创业成为主要创业形式,创业团队异质性对团队创造力的影响成为创业研究的重要议题。基于社会认知理论,将变革型领导和团队创新效能感纳入创业团队异质性与团队创造力关系模型中,构建一个有中介的调节模型。以珠三角高新科技园区创业团队为调研样本,运用结构方程模型方法实证研究创业团队异质性对团队创造力影响的内在机理。结果表明：创业团队异质性对团队创造力具有正向影响;团队创新效能感在创业团队异质性与团队创造力之间发挥中介作用;变革型领导在创业团队异质性与团队创新效能感的关系中发挥负向调节作用;变革型领导在创业团队异质性与团队创造力关系中发挥有中介的调节作用,这一调节作用通过团队创新效能感的中介实现。     

The constitutional political economy of virtual worlds

In virtual worlds, a social order able to coordinate the actions of tens of thousands of people emerges in a non-predetermined but designed way. The central puzzle the developers of such worlds have to solve is the same political economists face: to establish a well-functioning set of rules allowing for the thriving of the regulated community. The purpose of this paper is to provide a discussion of the particularities of the constitutional political economy of virtual worlds: their institutions, the prevalent beliefs of the players, and their organizations. The main reason why we should care about doing research on virtual worlds is the huge potential for research in virtual worlds. Virtual worlds present a middle ground in the debate between the greater control of laboratory experiments and the higher external validity of the field. Besides being an important cultural phenomenon per se, they emerge as the researchers’ tool to conduct experiments on a truly social level with tens of thousands of subjects. To show the usefulness of such environments for research in political economy in an exemplary but concrete fashion, the paper also presents some findings difficult to be produced elsewhere: data on an astonishingly high percentage of altruistic behavior in a Hobbesian natural state drawn from a dictator game played online.     

How Much Common Belief Is Necessary for a Convention?

We study Bayesian coordination games in which players choose actions conditional on the realization of their respective signals. Due to differential information, the players do not have common knowledge that a particular game is being played. However, they do have common beliefs with specified probabilities concerning their environment. In our framework, any equilibrium set of rules must be simple enough so that the actions of all players are common belief with probability 1 at every state. Common belief with probability close to 1 will not do.Journal of Economic LiteratureClassification Numbers: C72, D82.     

Asymmetric memory recall of positive and negative events in social interactions

Previous studies have suggested that negative emotion can enhance memory accuracy. However, they were not conducted in the context of social interactions using the methodology of experimental economics. Based on the present study, we find that in such a context, individuals’ memory recall accuracy depends on the kindness of acts and who performed them, and negative emotion may lower memory accuracy. A victim of an unkind act is more likely to forget than someone who benefited from a kind act. This result supports the hypothesis that individuals may strategically manipulate their memory by forgetting an unpleasant experience. We also find that individuals who committed an unkind act tend to perceive it as less unkind as time moves on. They also tend to believe that a higher percentage of players have also committed the unkind act. Overall, the results support the hypothesis that individuals strategically manipulate their memory and beliefs to maintain self-esteem or feel less guilty.     

On Sugden’s “mutually beneficial practice” and Berge equilibrium

Cooperative behavior is often observed in ordinary market transactions. To account for this observation, Robert Sugden proposes a team reasoning theory in which the common interest of team reasoners is defined by the notion of mutually beneficial practice. We study the relationships between mutually beneficial practices and Berge equilibria (a Berge equilibrium is a strategy profile such that a unilateral change of strategy by any one player cannot increase another player’s payoff). We propose two sufficient conditions under which a (strict) Berge equilibrium is a mutually beneficial practice.     

Self-referential thinking and equilibrium as states of mind in games: fMRI evidence

Sixteen subjects' brain activity were scanned using fMRI as they made choices, expressed beliefs, and expressed iterated 2nd-order beliefs (what they think others believe they will do) in eight games. Cingulate cortex and prefrontal areas (active in “theory of mind” and social reasoning) are differentially activated in making choices versus expressing beliefs. Forming self-referential 2nd-order beliefs about what others think you will do seems to be a mixture of processes used to make choices and form beliefs. In equilibrium, there is little difference in neural activity across choice and belief tasks; there is a purely neural definition of equilibrium as a “state of mind.” “Strategic IQ,” actual earnings from choices and accurate beliefs, is negatively correlated with activity in the insula, suggesting poor strategic thinkers are too self-focused, and is positively correlated with ventral striatal activity (suggesting that high IQ subjects are spending more mental energy predicting rewards).     

Coordination,timing and common knowledge

There is tight link between coordination and common knowledge. The role of higher order beliefs in static incomplete information games has been widely studied. In particular, information frictions break down common knowledge. A large body of literature in economics examine dynamic coordination problems when there are timing frictions, in the sense that players do not all move at once. Timing frictions in dynamic coordination games play a role that is closely analogous to information frictions in static coordination games.This paper makes explicit the role of higher order beliefs about timing in dynamic coordination games with timing frictions. An event is said to be effectively known if a player knew the event when he last had an option to change his behavior. The lack of effective common knowledge of the time drives results of dynamic coordination games.     

Interactive team reasoning: A contribution to the theory of co-operation

This paper describes interactions between agents who sometimes choose as individuals and sometimes as members of teams. Choosing as a member of a team entails not only being motivated by the team's objective, but also a distinctive pattern of reasoning: an agent who “team reasons” computes, and chooses her component in, aprofile evaluated using the team's objective function. It is not assumed that a given agent team reasons for a particular team; there may be more than one team, and which she reasons for is here treated probabilistically. Ordinary reasoning is a special case in which the team is a singleton. The framework therefore encompasses interactions paradigmatic in the theory of co-operative behaviour in which agents may choose either for the group of for themselves. The hypothesis that people may team reason if and when they are group motivated can, it is shown, explain some puzzling aspects of co-operative behaviour in a new way.     

Mindreading and endogenous beliefs in games

We argue that a Bayesian explanation of strategic choices in games requires introducing a psychological theory of belief formation. We highlight that beliefs in epistemic game theory are derived from the actual choice of the players, and cannot therefore explain why Bayesian rational players should play the strategy they actually chose. We introduce the players’ capacity of mindreading in a game theoretical framework with the simulation theory, and characterise the beliefs that Bayes rational players could endogenously form in games. We show in particular that those beliefs need not be ratifiable, and therefore that rational players can form action-dependent beliefs.     

Prior symmetry, similarity-based reasoning, and endogenous categorization

This paper presents a rational theory of categorization and similarity-based reasoning. I study a model of sequential learning in which the decision maker infers unknown properties of an object from information about other objects. The decision maker may use the following heuristics: divide objects into categories with similar properties and predict that a member of a category has a property if some other member of this category has this property. The environment is symmetric: the decision maker has no reason to believe that the objects and properties are a priori different. In symmetric environments, categorization is an optimal solution to an inductive inference problem. Any optimal solution looks as if the decision maker categorizes. Various experimental observations about similarity-based reasoning coincide with the optimal behavior in my model.     

Bayesian learning and convergence to Nash equilibria without common priors

Summary. Consider an infinitely repeated game where each player is characterized by a “type” which may be unknown to the other players in the game. Suppose further that each player's belief about others is independent of that player's type. Impose an absolute continuity condition on the ex ante beliefs of players (weaker than mutual absolute continuity). Then any limit point of beliefs of players about the future of the game conditional on the past lies in the set of Nash or Subjective equilibria. Our assumption does not require common priors so is weaker than Jordan (1991); however our conclusion is weaker, we obtain convergence to subjective and not necessarily Nash equilibria. Our model is a generalization of the Kalai and Lehrer (1993) model. Our assumption is weaker than theirs. However, our conclusion is also weaker, and shows that limit points of beliefs, and not actual play, are subjective equilibria. Received: March 3, 1995; revised version: February 17, 1997     

Between-game rule learning in dissimilar symmetric normal-form games

Rule learning posits that decision makers, rather than choosing over actions, choose over behavioral rules with different levels of sophistication. Rules are reinforced over time based on their historically observed payoffs in a given game. Past works on rule learning have shown that when playing a single game over a number of rounds, players can learn to form sophisticated beliefs about others. Here we are interested in learning that occurs between games where the set of actions is not directly comparable from one game to the next. We study a sequence of ten thrice-played dissimilar games. Using experimental data, we find that our rule learning model captures the ability of players to learn to reason across games. However, this learning appears different from within-game rule learning as previously documented. The main adjustment in sophistication occurs by switching from non-belief-based strategies to belief-based strategies. The sophistication of the beliefs themselves increases only slightly over time.