Asymmetric Information in Simple Bargaining Games: An Experimental Study

Bilateral bargaining situations are often characterized by informational asymmetries concerning the size of what is at stake: in some cases, the proposer is better informed, in others, it is the responder. We analyze the effects of both types of asymmetric information on proposer behavior in two different situations which allow for a variation of responder veto power: the ultimatum and the dictator game. We find that the extent to which proposers demand less in the ultimatum as compared to the dictator game is (marginally) smaller when the proposer is in the superior information position. Further we find informed proposers to exploit their informational advantage by offering an amount that does not reveal the true size of the pie, with proposers in the ultimatum game exhibiting this behavioral pattern to a larger extent than those in the dictator game. Uninformed proposers risk imposed rejection when they ask for more than potentially is at stake, and ask for a risk premium in dictator games. We concentrate on proposers, but also explore responder behavior: We find uninformed responders to enable proposers’ hiding behavior, and we find proposer intentionality not to play an important role for informed responders when they decide whether to accept or reject an offer by an (uninformed) proposer.     

Behavioral spillovers and cognitive load in multiple games: An experimental study

We present evidence from laboratory experiments of behavioral spillovers and cognitive load that spread across strategic contexts. In the experiments, subjects play two distinct games simultaneously with different opponents. We find that the strategies chosen and the efficiency of outcomes in one game depends on the other game that the subject plays, and that play is altered in predictable directions. We develop a measure of behavioral variation in a normal form game, outcome entropy, and find that prevalent strategies in games with low outcome entropy are more likely to be used in the games with high outcome entropy, but not vice versa. Taken together, these findings suggest that people do not treat strategic situations in isolation, but may instead develop heuristics that they apply across games.     

Trading with a common agent under complete information: A characterization of Nash equilibria

We analyze an abstract model of trading where N principals submit quantity-payment schedules that describe the contracts they offer to an agent, and the agent then chooses how much to trade with every principal. This represents a special class of common agency games with complete information. We study all the subgame perfect Nash equilibria of these games, not only truthful ones, providing a complete characterization of equilibrium payoffs. In particular, we show that the equilibrium that is Pareto-dominant for the principals is not truthful when there are more than two of them. We also provide a partial characterization of equilibrium strategies.     

Who knows it is a game? On strategic awareness and cognitive ability

We examine strategic awareness in experimental games, that is, the question of whether subjects realize they are playing a game and thus have to form beliefs about others’ actions. We conduct a beauty contest game and elicit measures of cognitive ability and beliefs about others’ cognitive ability. We show that the effect of cognitive ability is highly non-linear. Subjects below a certain threshold choose numbers in the whole interval and their behavior does not correlate with beliefs about others’ ability. In contrast, subjects who exceed the threshold avoid choices above 50 and react very sensitively to beliefs about the cognitive ability of others.     

Does seeing more deeply into a game increase one’s chances of winning?

The substantively rational value of the games studied in this paper does not help predict subject performance in the experiment at all. An accurate model must account for the cognitive ability of the people playing the game. This paper investigates whether the variation in measured rationality bounds is correlated with the probability of winning when playing against another person in games that exceed both players’ estimated rationality bound. Does seeing deeper into a game matter when neither player can see to the end of the game? Subjects with higher measured bounds win 63 percent of the time and the larger the difference the more frequently they win.     

Cultural Differences in Ultimatum Game Experiments: Evidence from a Meta-Analysis

This paper reports the findings of a meta-analysis of 37 papers with 75 results from ultimatum game experiments. We find that on average the proposer offers 40% of the pie to the responder. This share is smaller for larger pie sizes and larger when a strategy method is used or when subjects are inexperienced. On average 16% of the offers is rejected. The rejection rate is lower for larger pie sizes and for larger shares offered. Responders are less willing to accept an offer when the strategy method is employed. As the results come from different countries, meta-analysis provides an alternative way to investigate whether bargaining behavior in ultimatum games differs across countries. We find differences in behavior of responders (and not of proposers) across geographical regions. With one exception, these differences cannot be attributed to various cultural traits on which for instance the cultural classifications of Hofstede (1991) and Inglehart (2000) are based.     

Lexicographic composition of simple games

Certain voting bodies can be modeled as a simple game where a coalition's winning depends on whether it wins, blocks or loses in two smaller simple games. There are essentially five such ways to combine two proper games into a proper game. The most decisive is the lexicographic rule, where a coalition must either win in G₁, or block in G₁ and win in G₂. When two isomorphic games are combined lexicographically, a given role for a player confers equal or more power when held in the first game than the second, if power is assessed by any semi-value. A game is lexicographically separable when the players of the two components partition the whole set. Games with veto players are not separable, and games of two or more players with identical roles are separable only if decisive. Some separable games are egalitarian in that they give players identical roles.     

Efficiency results in N player games with imperfect private monitoring

We demonstrate that efficiency is achievable in a certain class of N player repeated games with private, almost perfect monitoring. Our equilibrium requires only one period memory and can be implemented by two state automata. Furthermore, we show that this efficiency result holds with any degree of accuracy of monitoring if private signals are hemiindependent. Whereas most existing research focuses on two player cases or only a special example of N player games, our results are applicable to a wide range of N player games of economic relevance, such as trading goods games and price-setting oligopolies.     

Transparency and cooperation in repeated dilemma games: a meta study

We use data from experiments on finitely repeated dilemma games with fixed matching to investigate the effect of different types of information on cooperation. The data come from 71 studies using the voluntary contributions paradigm, covering 122 data points, and from 18 studies on decision-making in oligopoly, covering another 50 data points. We find similar effects in the two sets of experimental games. We find that transparency about what everyone in a group earns reduces contributions to the public good, as well as the degree of collusion in oligopoly markets. In contrast, transparency about choices tends to lead to an increase in contributions and collusion, although the size of this effect varies somewhat between the two settings. Our results are potentially useful for policy making, because they provide guidance on the type of information to target in order to stimulate or limit cooperation.     

Competitive behavior in market games: Evidence and theory

We explore whether competitive outcomes arise in an experimental implementation of a market game, introduced by Shubik (1973) [21]. Market games obtain Pareto inferior (strict) Nash equilibria, in which some or possibly all markets are closed. We find that subjects do not coordinate on autarkic Nash equilibria, but favor more efficient Nash equilibria in which all markets are open. As the number of subjects participating in the market game increases, the Nash equilibrium they achieve approximates the associated competitive equilibrium of the underlying economy. Motivated by these findings, we provide a theoretical argument for why evolutionary forces can lead to competitive outcomes in market games.     

Bargaining with Imperfect Commitment

We study the effect of imperfect commitment in noncooperative two-person bargaining games. By establishing the reputation for being stubborn, a player sometimes commits to her initial demand, becoming unable to change her demands or to accept an inferior offer from her opponent. When the probability of being stubborn is small, the set of equilibria is shown to be small and agreement may be reached immediately despite the possibility of stubbornness. A player has greater bargaining power when she is more patient and/or is more likely to be stubborn. Journal of Economic Literature Classification Number: C78.     

A model of political parties

This paper presents a new model of political parties. I assume that the role of parties is to increase the commitment ability of politicians vis-à-vis the voters. Whereas a politician running alone can only offer his ideal policy, the set of policies that a party can commit to is the Pareto set of its members. I show that the commitment mechanisms provided by the institution of parties has no effect when the policy space is unidimensional; the policies parties can induce in equilibrium arise also when politicians are running independently. However, when the policy space is multidimensional, politicians use the vehicle of parties to offer equilibrium policies that they cannot offer in their absence.     

Core tâtonnement

Two discrete time tâtonnement processes—one featuring successive tâtonnement, the other featuring simultaneous tâtonnement—for the core of coalitional games with transferable utility are introduced. For totally balanced games, the successive core tâtonnement process corresponds to the standard simultaneous price tâtonnement process of competitive equilibrium theory via the Shapley-Shubik (market game-direct market) correspondence. The simultaneous core tâtonnement process is based entirely on the intuition behind the definition of the core for games with transferable utility, and it does not correspond to any evident competitive equilibrium tâtonnement process. Both processes are proven to be globally stable. The two processes offer easily implementable algorithms for approximately computing core points.     

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.     

Learning in experimental games

Summary Experimental games typically involve subjects playing the same game a number of times. In the absence of perfect rationality by all players, the subjects may use the behavior of their opponents in early rounds to learn about the extent of irrationality in the population they face. This makes the problem of finding the Bayes-Nash equilibrium of the experimental game much more complicated than finding the game-theoretic solution to the ideal game without irrationality. We propose and implement a computationally intensive algorithm for finding the equilibria of complicated games with irrationality via the minimization of an appropriate multi-variate function. We propose two hypotheses about how agents learn when playing experimental games. The first posits that they tend to learn about each opponent as they play it repeatedly, but do not learn about the population parameters through their observations of random opponents (myopic learning). The second posits that both types of learning take place (sequential learning). We introduce a computationally intensive sequential procedure to decide on the informational value of conducting additional experiments. With the help of that procedure, we decided after 12 experiments that our original model of irrationality was unsatisfactory for the purpose of discriminating between our two hypotheses. We changed our models, allowing for two different types of irrationality, reanalyzed the old data, and conducted 7 more experiments. The new model successfully discriminated between our two hypotheses about learning. After only 7 more experiments, our approximately optimal stopping rule led us to stop sampling and accept the model where both types of learning occur.We acknowledge the financial support from NSF grant #SES9011828 to the California Institute of Technology. We also acknowledge the able research assistance of Mark Fey, Lynell Jackson and Jeffrey Prisbrey in setting up the experiments, recruiting subjects and running the experiments. We acknowledge the help of the Jet Propulsion Laboratory and its staff members for giving us access to their Cray XMP/18, and subsequently their Cray YMP2E/116.     

Viewpoint: On the generalizability of lab behaviour to the field

Abstract.  We can think of no question more fundamental to experimental economics than understanding whether, and under what circumstances, laboratory results generalize to naturally occurring environments. In this paper, we extend Levitt and List (2006) to the class of games in which financial payoffs and 'doing the right thing' are not necessarily in conflict. We argue that behaviour is crucially linked to not only the preferences of people, but also the properties of the situation. By doing so, we are able to provide a road map of the psychological and economic properties of people and situations that might interfere with generalizability of laboratory result from a broad class of games.     

On Perceptions of Fairness: The Role of Valuations, Outside Options, and Information in Ultimatum Bargaining Games

This study examines fairness perceptions in ultimatum bargaining games with asymmetric payoffs, outside options, and different information states. Fairness perceptions were dependent on treatment conditions. Specifically, when proposers had higher chip values, dollar offers were lower than when responders had higher chip values. When responders had an outside option, offers were higher and were rejected less often than when proposers had an outside option. However, a given offer was rejected more often when responders had an outside option. Therefore, similar to the first mover advantage, the “advantaged” or “entitled” player received a higher monetary payoff than they would otherwise. When there was complete information about payoff amounts (payoff conversion rates and outside options), rejections occurred more often, and given offer amounts were rejected more often than when there was incomplete information. When there was incomplete information, offers were higher in the initial rounds than in the final rounds. These results suggest that proposers made offers strategically, making offers that would not be rejected, rather than out of a concern for fairness.     

Higher cognitive ability is associated with lower entries in a p-beauty contest

“Beauty contests” are well-studied, dominance-solvable games that generate two interesting results. First, most behavior does not conform to the unique Nash equilibrium. Second, there is considerable unexplained heterogeneity in behavior. In this work, we explore the relationship between beauty contest behavior and cognitive ability. We find that subjects with high cognitive ability exhibit behavior that is closer to the Nash equilibrium.     

Diminished-dimensional political economy

Economists base policy advice on models of responses by a variety of economic entities to policy adoptions. There is compelling evidence that these entities do not optimize as mainstream economics assumes. Rather, they limit decision-making to solving problems of much smaller dimensionality. We consider how political economy goes awry when ignoring diminished dimensionality, and some research avenues opened up by this realization.     

Personality and cooperation in finitely repeated prisoner’s dilemma games

We investigate the role personality plays in Finitely Repeated Prisoner’s Dilemma (FRPD) games. Even after controlling for demographic factors such as race, course of study, and cognitive ability, we find that cooperative behavior is significantly related to the Big Five personality trait Agreeableness. A one standard deviation increase in agreeableness increases the predicted probability of cooperation by a subject with modal demographic characteristics from 67.9% to 80.6%.