Belief in the opponentsʼ future rationality

For dynamic games we consider the idea that a player, at every stage of the game, will always believe that his opponents will choose rationally in the future. This is the basis for the concept of common belief in future rationality, which we formalize within an epistemic model. We present an iterative procedure, backward dominance, that proceeds by eliminating strategies from the game, based on strict dominance arguments. We show that the backward dominance procedure selects precisely those strategies that can rationally be chosen under common belief in future rationality if we would not impose (common belief in) Bayesian updating.     

Technology adoption in markets with network effects: Theory and experimental evidence

We examine a technology-adoption game with network effects in which coordination on either technology A or technology B constitutes a Nash equilibrium. Coordination on technology B is assumed to be payoff dominant. We define a technology’s critical mass as the minimal share of users, which is necessary to make the choice of this technology the best response for any remaining user. We show that the technology with the lower critical mass implies risk dominance and selection by the maximin criterion. We present experimental evidence that both payoff dominance and risk dominance explain participants’ choices in the technology-adoption game. The relative riskiness of a technology can be proxied using either technologies’ critical masses or stand-alone values absent any network effects.     

Cognitive bubbles

Smith et al. (Econometrica 56(5):1119, 1988) reported large bubbles and crashes in experimental asset markets, a result that has been replicated many times. Here we test whether the occurrence of bubbles depends on the experimental subjects’ cognitive sophistication. In a two-part experiment, we first run a battery of tests to assess the subjects’ cognitive sophistication and classify them into low or high levels. We then invite them separately to two asset market experiments populated only by subjects with either low or high cognitive sophistication. We observe classic bubble and crash patterns in markets populated by subjects with low levels of cognitive sophistication. Yet, no bubbles or crashes are observed with our sophisticated subjects, indicating that cognitive sophistication of the experimental market participants has a strong impact on price efficiency.     

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.     

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.     

Cooperation by Asymmetric Agents in a Joint Project

The object of study is cooperation in joint projects where agents may have different desired sophistication levels for the project and where some of the agents may have low budgets. In this context, questions concerning the optimal realizable sophistication level and the distribution of the related costs among the participants are tackled. A related cooperative game, the enterprise game, and a non‐cooperative game, the contribution game, are both helpful. It turns out that there is an interesting relation between the core of the convex enterprise game and the set of strong Nash equilibria of the contribution game. Special attention is paid to a new rule inspired by the Baker–Thompson rule in the airport landing fee literature. For this rule, the project is split up in a sequence of subprojects where the involved participants pay amounts which are, roughly speaking, equal, but not more than their budgets allow. The resulting payoff distribution turns out to be a core element of the related enterprise game.     

Circadian effects on strategic reasoning

The ability to strategically reason is important in many competitive environments. In this paper, we examine how relatively mild temporal variations in cognition affect reasoning in the Beauty Contest. The source of temporal cognition variation that we explore is the time-of-day that decisions are made. Our first result is that circadian mismatched subjects (i.e., those making decisions at off-peak time of day) display lower levels of strategic reasoning in the p<1 Beauty Contest but not in the p>1 game. This suggests that a cognitively more challenging environment is required for circadian mismatch to harm strategic reasoning. A?second result is that choice adaptation or mimicry (i.e., a?more automatic type of responding than what is typically considered to be “learning”) during repeated play is not significantly affected by circadian mismatch. This is consistent with the hypothesis that automatic thought is more resilient to cognitive resource depletion than controlled-thought decision making.     

Von Neumann-Morgenstern solution social choice functions: An impossibility theorem

Recent literature has made significant progress in characterizing those social choice functions that can arise, or be “implemented,” as the equilibria of an underlying noncooperative game. This paper studies the implementability of social choice functions via cooperative games. Specifically, we show that if a social choice function arises, in each environment, as a Von Neumann-Morgenstern solution of an underlying cooperative game, whose dominance structure is monotonic and neutral, then the social choice function is essentially oligarchic, in exactly the same sense that “core” selecting choice functions are oligarchic.     

Equilibrium selection in global games with strategic complementarities

We study games with strategic complementarities, arbitrary numbers of players and actions, and slightly noisy payoff signals. We prove limit uniqueness: as the signal noise vanishes, the game has a unique strategy profile that survives iterative dominance. This generalizes a result of Carlsson and van Damme (Econometrica 61 (1993) 989-1018) for two-player, two-action games. The surviving profile, however, may depend on fine details of the structure of the noise. We provide sufficient conditions on payoffs for there to be noise-independent selection.     

Individual Characteristics and the Disposition Effect: The Opposing Effects of Confidence and Self-Regard

We conduct two experiments to examine potential causes of the disposition effect. In Experiment 1, we rule out beliefs in mean reversion as a cause of the disposition effect. Although a belief in the mean reversion of stock prices should be independent of whether an investor owns or only follows the stock, we show only investors who own the stock behave as though prices will reverse. In Experiment 2, participants buy and sell securities over multiple periods. We find that self-regard and investing confidence (two types of self-esteem) have opposing influences on investors’ tendency to hold losing investments. Investors with lower self-regard hold losing investments longer than those with higher self-regard, and investors with higher confidence hold losing investments longer than those with lower confidence. We focus on investors’ tendency to hold losing stocks too long because prior research suggests the gain versus loss sides of the disposition effect are driven by different biases.     

The control of game form recognition in experiments: understanding dominant strategy failures in a simple two person “guessing” game

This paper focuses on instructions and procedures as the reasons that subjects fail to behave according to the predictions of game theory in two-person “guessing game” (beauty contest game) experiments. In this game, two individuals simultaneously choose a number between 0 and 100. The winner is the person whose chosen number is the closest to 2/3 of the average of the two numbers. The weakly dominant strategy is zero. Because of the simplicity of the game, the widespread failure of subjects to choose the weakly dominant strategy has been interpreted as evidence of some fundamental inability to behave strategically. By contrast, we find that subjects’ behavior reflects a lack of understanding of the game form, which we define as the relationships between possible choices, outcomes and payoffs. To a surprising degree, subjects seem to have little understanding of the experimental environment in which they are participating. If subjects do not understand the game form, the experimental control needed for testing game theory is lost. The experiments reported here demonstrate that the failure to act strategically is related to how the game is presented. We test how well subjects are able to recognize the game under a variety of different presentations of the game. Some subjects fail to recognize the game form when it is presented abstractly. When the game is transformed into a simple isomorphic game and presented in a familiar context, subjects do choose weakly dominant strategies. While our results confirm the ability of subjects to make strategic decisions, they also emphasize the need to understand the limitations of experimental subjects’ ability to grasp the game as the experimenter intends. Given these limitations, we provide suggestions for better experimental control.     

Overcoming coordination failure using a mechanism based on gradualism and endogeneity

We examine three tools that can enhance coordination success in a repeated multiple-choice coordination game. Gradualism means that the game starts as an easy coordination problem and moves gradually to a more difficult one. The Endogenous Ascending mechanism implies that a gradual increase in the upper bound of coordination occurs only if coordination with the Pareto superior equilibrium in a stage game is attained. The Endogenous Descending mechanism requires that when the game’s participants fail to coordinate, the level of the next coordination game be adjusted such that the game becomes simpler. We show that gradualism may not always work, but in such instances, its effect can be reinforced by endogeneity. Our laboratory experiment provides evidence that a mechanism that combines three tools, herein termed the “Gradualism with Endogenous Ascending and Descending (GEAD)” mechanism, works well. We discuss how the GEAD mechanism can be applied to real-life situations that suffer from coordination failure.     

Keeping others in our mind or in our heart? Distribution games under cognitive load

It has recently been argued that giving is spontaneous while greed is calculated (Rand et al., in Nature 489:427–430, 2012). If greed is calculated we would expect that cognitive load, which is assumed to reduce the influence of cognitive processes, should affect greed. In this paper we study both charitable giving and the behavior of dictators under high and low cognitive load to test if greed is affected by the load. This is tested in three different dictator game experiments. In the dictator games we use both a give frame, where the dictators are given an amount that they may share with a partner, and a take frame, where dictators may take from an amount initially allocated to the partner. The results from all three experiments show that the behavioral effect in terms of allocated money of the induced load is small if at all existent. At the same time, follow-up questions indicate that the subjects’ decisions are more impulsive and less driven by their thoughts under cognitive load.     

Does competition foster trust? The role of tournament incentives

Members of organizations are often called upon to trust others and to reciprocate trust while at the same time competing for bonuses or promotions. We suggest that competition affects trust not only within dyads including direct competitors, but also between individuals who do not compete against each other. We test this idea in a trust game where trustors and trustees are rewarded based either on their absolute performance or on how well they do relative to players from other dyads. In Experiment 1, we show that competition among trustors significantly increases trust. Competition among trustees decreases trustworthiness, but trustors do not anticipate this effect. In Experiment 2, we additionally show that the increase in trust under competition is caused by a combination of increased risk taking and lower sensitivity to non-financial concerns specific to trust interactions. Our results suggest that tournament incentives might have a “blinding effect” on considerations such as betrayal and inequality aversion.     

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.     

Dominance solvability of dynamic bargaining games

We formulate and study a general finite-horizon bargaining game with simultaneous moves and a disagreement outcome that need not be the worst possible result for the agents. Conditions are identified under which the game is dominance solvable in the sense that iterative deletion of weakly dominated strategies selects a unique outcome. Our analysis uses a backward induction procedure to pinpoint the latest moment at which a coalition can be found with both an incentive and the authority to force one of the available alternatives. Iterative dominance then implies that the alternative characterized in this way will be agreed upon at the outset—or, if a suitable coalition is never found, that no agreement will be reached.     

Payoff dominance and risk dominance in the observable delay game: a note

We examine whether the payoff dominant sequential-move (Stackelberg) outcome is realized when timing is endogenized. We adopt the observable delay game formulated by Hamilton and Slutsky [Games Econ Behav 2(1):29–46, 1990]. We find that if one sequential-move outcome is payoff dominant, either (i) the outcome both players prefer is the unique equilibrium; or (ii) two sequential-move outcomes are equilibria and the one both players prefer is risk dominant. In other words, no conflict between payoff dominance and risk dominance in the observable delay game exists, in contrast to other games such as (non pure) coordination games. We also find that even if one of two sequential-move outcomes is the unique equilibrium outcome in the observable delay game, it does not imply that the equilibrium outcome is payoff dominant to the other sequential-move outcome.      

Equilibrium selection through incomplete information in coordination games: an experimental study

We perform an experiment on a pure coordination game with uncertainty about the payoffs. Our game is closely related to models that have been used in many macroeconomic and financial applications to solve problems of equilibrium indeterminacy. In our experiment, each subject receives a noisy signal about the true payoffs. This game (inspired by the “global” games of Carlsson and van Damme, Econometrica, 61, 989–1018, 1993) has a unique strategy profile that survives the iterative deletion of strictly dominated strategies (thus a unique Nash equilibrium). The equilibrium outcome coincides, on average, with the risk-dominant equilibrium outcome of the underlying coordination game. In the baseline game, the behavior of the subjects converges to the theoretical prediction after enough experience has been gained. The data (and the comments) suggest that this behavior can be explained by learning. To test this hypothesis, we use a different game with incomplete information, related to a complete information game where learning and prior experiments suggest a different behavior. Indeed, in the second treatment, the behavior did not converge to equilibrium within 50 periods in some of the sessions. We also run both games under complete information. The results are sufficiently similar between complete and incomplete information to suggest that risk-dominance is also an important part of the explanation.      

Collective Choice in the Commons: Experimental Results on Proposed Allocation Rules and Votes

We analyse and empirically examine a multi-level common-pool resource (CPR) game consisting of a collective-choice level game and an operational-level game. In the collective-choice game, participants anonymously propose allocation rules to be used in the operational game and vote anonymously on the proposed rules. Majority and unanimity rules are investigated. Our major finding is that both types of voting rules substantially increase efficiency relative to a baseline with no opportunity for collective choice, but the distributional consequences of the rules differ. To understand the process by which efficiency is improved better, we examine four predictive theories related to proposals, votes, and outcomes.