Mixed-strategy equilibria in the Nash Demand Game

In the Nash Demand Game, each of the two players announces the share he demands of an amount of money that may be split between them. If the demands can be satisfied, they are; otherwise, neither player receives any money. This game has many pure-strategy equilibria. This paper characterizes mixed-strategy equilibria. The condition critical for an equilibrium is that players’ sets of possible demands be balanced. Two sets of demands are balanced if each demand in one set can be matched with a demand in the other set such that they sum to one. For Nash’s original game, a complete characterization is given of the equilibria in which both players’ expected payoffs are strictly positive. The findings are applied to the private provision of a discrete public good.     

In search of an evolutionary edge: trading with a few, more, or many

Consider a population of farmers who live around a lake. Each farmer engages in trade with his m adjacent neighbors, where m is termed the “span of interaction.” Trade is governed by a prisoner’s dilemma “rule of engagement.” A farmer’s payoff is the sum of the payoffs from the m prisoner’s dilemma games played with his ^m/₂^m/_2 neighbors to the left, and with his ^m/₂^m/_2 neighbors to the right. When a farmer dies, his son takes over. The son who adheres to his father’s span of interaction decides whether to cooperate or defect by considering the actions taken and the payoffs received by the most prosperous member of the group comprising his father and his father’s m trading partners. Under a conventional structure of payoffs, it is shown that a large span of interaction is detrimental to the long-run coexistence of cooperation and defection, and conditions are provided under which the social outcome associated with the expansion of trade when individuals trade with a few is better than that when they trade with many. Under the stipulated conditions it is shown, by means of a static comparative analysis of the steady state configurations of the farmer population, that an expansion of the market can be beneficial in one context, detrimental in another.     

Are we nice(r) to nice(r) people?—An experimental analysis

We experimentally investigate whether individuals can reliably detect cooperators (the nice(r) people) in an anonymous decision environment involving “connected games.” Participants can condition their choices in an asymmetric prisoners’ dilemma and a trust game on past individual (their partner’s donation share to a self-selected charity) and social (whether their partner belongs to a group with high or low average donations) information. Thus, the two measures of niceness are the individual donation share in the donation task, and the cooperativeness of one’s choice in the two games. We find that high donors achieve a higher-than-average expected payoff by cooperating predominantly with other high donors. Group affiliation proved to be irrelevant. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C91, C72, D3     

Individual Rationality and the “Zonal Attachment” Principle: Three Stock Migration Models

Shared fish stocks migrate across borders between different countries’ exclusive economic zones. This paper discusses the individual rationality of fish-sharing agreements based on the zonal attachment of such stocks. Three types of migrations are considered: (i) a common stock that grows and reproduces and is then distributed in given proportions between two countries’ zones at the beginning of each fishing season; (ii) sub-stocks that breed and grow independently in their separate zones but spill over between zones according to relative abundance; (iii) a stock that grows and breeds in one country’s zone but migrates into the zone of another if it exceeds a certain size. It is shown that in all these cases the minor partner in a fish-sharing agreement may not have an incentive to cooperate unless he gets a larger share of the cooperative profits than that corresponds to his share of the stock. This is particularly likely to happen when the unit cost of fish does not depend on the stock. An exception could occur if stock migration depends on the stock level; the major partner could then keep the entire stock by fishing it down to a critical level.     

Self-interest and fairness: self-serving choices of justice principles

We introduce non-enforceable property rights over a bargaining surplus in a dictator game with production, where the agent’s effort is differentially rewarded and subsequently determines the size of the surplus. Using experimental data, we elicit individual preferences over the egalitarian, accountability and libertarian principles and provide evidence to support the inability of these justice principles to individually account for the observed behavior. We show that the justice principle that can be used to explain dictators’ choices depends on whether dictators are paid more or less than recipients for their effort. Our findings suggest that dictators do employ justice principles in self-serving ways and choose in each context the justice principle that maximizes their financial payoffs.     

An evolutionary edge of knowing less (or: On the ‘curse’ of global information)

Consider a population of farmers who live around a lake. Each farmer engages in trade with his two adjacent neighbors. The trade is governed by a prisoner’s dilemma ‘rule of engagement.’ A farmer’s payoff is the sum of the payoffs from the two prisoner’s dilemma games played with his two neighbors. When a farmer dies, his son takes over. The son decides whether to cooperate or defect by considering the actions taken and the payoffs received by the most prosperous members of the group comprising his own father and a set of his father’s neighbors. The size of this set, which can vary, is termed the ‘span of information.’ It is shown that a larger span of information can be detrimental to the stable coexistence of cooperation and defection, and that in well-defined circumstances, a large span of information leads to an end of cooperation, whereas a small span does not. Conditions are outlined under which, when individuals’ optimization is based on the assessment of less information, the social outcome is better than when optimization is based on an assessment of, and a corresponding response to, more information.     

From ultimatum to Nash bargaining: Theory and experimental evidence

We consider a sequential two-party bargaining game with uncertain information transmission. When the first mover states her demand she does only know the probability with which the second mover will be informed about it. The informed second mover can either accept or reject the offer and payoffs are determined as in the ultimatum game. Otherwise the uninformed second mover states his own demand and payoffs are determined as in the Nash demand game. In the experiment we vary the commonly known probability of information transmission. Our main finding is that first movers’ and uninformed second movers’ demands adjust to this probability as qualitatively predicted, that is, first movers’ (uninformed second movers’) demands are lower (higher) the lower the probability of information transmission. JEL Classification C72 · C78 · C92     

Observability and overcoming coordination failure in organizations: An experimental study

Motivated by problems of coordination failure in organizations, we examine how overcoming coordination failure and maintaining coordination depend on the ability of individuals to observe others’ choices. Subjects’ payoffs depend on coordinating at high effort levels in a weak-link game. Treatments vary along two dimensions. First, subjects either start with low financial incentives for coordination, which typically leads to coordination failure, and then are switched to higher incentives or start with high incentives, which usually yield effective coordination, and are switched to low incentives. Second, as the key treatment variable, subjects either observe the effort levels chosen by all individuals in their experimental group (full feedback) or observe only the minimum effort (limited feedback). We find three primary results: (1) When starting from coordination failure the use of full feedback improves subjects’ ability to overcome coordination failure, (2) When starting with good coordination the use of full feedback has no effect on subjects’ ability to avoid slipping into coordination failure, and (3) History-dependence, defined as dependence of current effort levels on past incentives, is strengthened by the use of full feedback. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification C92, D23, J31, L23, M52     

The affectionate society: does competition for partners promote friendliness?

We study household formation in a model where collective consumption decisions of a household depend on the strategic choices of its members. The surplus of households is determined by individual choices of levels of friendliness to each other. A strategic conflict arises from a coupling condition that ceteris paribus, a person’s friendlier attitude reduces the individual’s influence in the household’s collective decision on how to divide the ensuing surplus. While partners in an isolated household choose the minimum level of friendliness, competition for partners tends to promote friendliness. We find that affluence does not buy affection, but can lead to withholding of affection by an affluent partner who can afford to do so. In general, the equilibrium degree of friendliness proves sensitive to the socio-economic composition of the population. We would like to thank Clive Bell, Edward Glaeser, Roger Lagunoff, Eva Terberger and seminar audiences in Berlin, Birmingham, Blacksburg, Exeter, Heidelberg, Manchester and at IHS in Vienna for helpful comments. We greatly appreciate the thoughtful comments of a referee.     

Spending Time and Money within the Household*

We consider, both theoretically and empirically, the allocation of time and money within the household. The research question is whether a married person who enjoys more leisure than their partner also receives more consumption (which seems to indicate the outcome of power within the household) or receives less consumption (which seems to indicate differing intrahousehold preferences). We develop a simple parametric structural model with household production that is tested on survey data. We find that relative wages have an impact on power. For leisure, this effect is dominated by a conventional wage effect, in which the partner who has the higher wage takes less leisure.     

Higher-order risk preferences in social settings

We study prudence and temperance (next to risk aversion) in social settings. Previous experimental studies have shown that these higher-order risk preferences affect the choices of individuals deciding privately on lotteries that only affect their own payoff. Yet, many risky and financially relevant decisions are made in the social settings of households or organizations. We elicit higher-order risk preferences of individuals and systematically vary how an individual’s decision is made (alone or while communicating with a partner) and who is affected by the decision (only the individual or the partner as well). In doing so, we can isolate the effects of other-regarding concerns and communication on choices. Our results reveal that the majority of choices are risk averse, prudent, and temperate across social settings. We also observe that individuals are influenced significantly by the preferences of a partner when they are able to communicate and choices are payoff-relevant for both of them.     

Accidental Bequests: A Curse for the Rich and a Boon for the Poor*

When accidental bequests signal otherwise unobservable individual characteristics, such as productivity and longevity, the population should be partitioned into two groups: those who do not receive an inheritance and those who do. The first tagged group receives a Mirrlees second‐best tax schedule; the second group, when its type is fully revealed, faces a first‐best tax schedule. Receiving an inheritance makes high‐ability types worse off and low‐ability types better off. High‐ability individuals face a bequest tax of more than 100 percent, while low‐ability types face a bequest tax that can be smaller, as well as larger, than 100 percent, and it might even be negative.     

Equilibrium existence and approximation of regular discontinuous games

Many conditions have been introduced to ensure equilibrium existence in games with discontinuous payoff functions. This paper introduces a new condition, called regularity, that is simple and easy to verify. Regularity requires that if there is a sequence of strategies converging to s* such that the players’ payoffs along the sequence converge to the best-reply payoffs at s*, then s* is an equilibrium. We show that regularity is implied both by Reny’s better-reply security and Simon and Zame’s endogenous sharing rule approach. This allows us to explore a link between these two distinct methods. Although regularity implies that the limits of e{\epsilon}-equilibria are equilibria, it is in general too weak for implying equilibrium existence. However, we are able to identify extra conditions that, together with regularity, are sufficient for equilibrium existence. In particular, we show how regularity allows the technique of approximating games both by payoff functions and space of strategies.     

Comparing group and individual decision-making in risky environments

This dissertation completes salient group and individual experiments in two environments that differ as to whether or not an evaluative criterion exists to judge subject performance. The first environment is lottery-choice. No such criterion exists in a lottery-choice environment. Subjects base their decisions on their preference for risk. A lottery-choice experiment consists of a menu of paired lottery choices structured so that the crossover point to the high-risk lottery can be used to infer the degree of risk aversion. The results show a significant interaction exists between subject composition and lottery winning-percentage. Groups are more likely than individuals to choose the “safe” lottery in the lowest winning-percentages, but less likely to choose the “safe” lottery in the highest winning-percentages. This effect is also present in the sequenced experiment. Further, the sequenced experiment shows that group discussion results in a significant increase in the group’s risk aversion from the average risk preference of its members. Finally, the sequenced experiment shows making a decision in the group phase has an immediate impact on subsequent individual decisions compared to the subject’s initial decisions. The second environment is resource allocation. A resource allocation experiment consists of subjects making repeated decisions of how to divide an endowment into two assets, one of which the payoff is unknown. An evaluative criterion to the resource allocation problem exists, as there is a specific allocation that maximizes payoffs. However, subjects must learn the solution through search. Experimental results show: 1) group performance in the resource allocation experiment is not significantly different than individuals; 2) the predictions from a local search model are more consistent with group decisions than the predictions from a global search model; and 3) group risk preferences elicited through a separate lottery-choice experiment are not indicative of their performance in the resource allocation experiment. Ph.D. Dissertation, Completed at Indiana University, Bloomington Dissertation Committee: Chair–Professor Arlington W. Williams, Indiana University, Bloomington Assistant Professor Hugh Kelley, Indiana University, Bloomington Associate Professor Susan K. Laury, Georgia State University Professor James M. Walker, Indiana University, Bloomington     

A game-theoretic model of coalition formation among primates

This paper models the coalition formation process among primates as a sequential game. The population consists of individuals having distinct social ranks which is determined by the individual’s resource holding potential. Each member of the population is interested in gaining access to a food resource, either individually or via a coalition. At any given stage of the game, a player can either propose a specific coalition or he can be proposed to in order to join one. Hence, the strategy of a player consists of a sequence of decisions regarding who to propose to for the formation of a coalition and which proposals to accept or reject. We derive the preferences of the players over the various coalition structures under the assumption that the probability of a coalition to obtain the resource is given by a logistic distribution as a function of relative strengths of the players. We show that, given the primates’ strategic behavior, a variety of different coalition structures can emerge in equilibrium.      

Learning and transfer in signaling games

We explore how learning to play strategically in one signaling game promotes strategic play in a related signaling game. Following convergence to a pooling equilibrium, payoffs are changed to only support separating equilibria. More strategic play is observed following the change in payoffs than for inexperienced subjects in control sessions, contrary to the prediction of a fictitious play learning model. Introducing a growing proportion of sophisticated learners, subjects who anticipate responders’ behavior following the change in payoffs, enables the model to capture the positive cross-game learning observed in the data. Research support form the National Science Foundation grant number SBR9809538 is gratefully acknowledged. We have received research support from Jo Ducey, Guillaume Frechette, Steve Lehrer, and Carol Kraker Stockman. We have benefitted from comments of Eric Bettinger, John Ham, Jim Rebeitzer, Bob Slonim and seminar participants at Case Western Reserve University, Ohio State University, the University of Mississippi, the University of Illinois, and Purdue University. The usual caveat applies.     

Similarities and differences when building trust: the role of cultures

We run an experiment in which students of different European nationalities are matched in groups of five and repeatedly choose with whom within their group they want to play a trust game. Participants observe of each other age, gender, nationality and number of siblings. The region of origin, “North” or “South” is a major determinant of success in the experiment. Participants tend to trust those they trusted before and who trusted them. We do not find evidence of regional discrimination per se. It is only the underlying and significant differences in behavior that translate through repeated interactions into differences in payoffs between the two regions.     

Structural holes in social networks

We consider a setting where every pair of players that undertake a transaction (e.g. exchange goods or information) creates a unit surplus. A transaction can take place only if the players involved have a connection. If the connection is direct the two players split the surplus equally, while if it is indirect then intermediate players also get an equal share of the surplus. Thus, individuals form links with others to create surplus, to gain intermediation rents, and to circumvent others who are trying to become intermediary.Our analysis clarifies the interplay between these forces in the process of strategic network formation. First, we show that, in the absence of capacity constraints on links, it leads to the emergence of a star network where a single agent acts as an intermediary for all transactions and enjoys significantly higher payoffs. Second, we study the implications of capacity constraints in the ability of agents to form links. In this case, distances between players must be long, which induces players who are “far off” to connect in order to avoid paying large intermediation rents. A cycle network then emerges, payoffs being equal across all players.