Explore the vast range of titles available.

This volume contains the proceedings of two AMS Special Sessions on The Mathematics of Decisions, Elections, and Games, held January 4, 2012, in Boston, MA, USA and January 11-12, 2013, in San Diego, CA, USA.Decision theory, voting theory, and game theory are three intertwined areas of mathematics that involve making optimal decisions under different contexts. Although these areas include their own mathematical results, much of the recent research in these areas involves developing and applying new perspectives from their intersection with other branches of mathematics, such as algebra, representation theory, combinatorics, convex geometry, dynamical systems, etc.The papers in this volume highlight and exploit the mathematical structure of decisions, elections, and games to model and to analyze problems from the social sciences.

Conflict can profoundly affect individuals and their groups. Oftentimes, conflict involves a clash between one side seeking change and increased gains through victory and the other side defending the status quo and protecting against loss and defeat. However, theory and empirical research largely neglected these conflicts between attackers and defenders, and the strategic, social, and psychological consequences of attack and defense remain poorly understood. To fill this void, we model (1) the clashing of attack and defense as games of strategy and reveal that (2) attack benefits from mismatching its target's level of defense, whereas defense benefits from matching the attacker's competitiveness. This suggests that (3) attack recruits neuroendocrine pathways underlying behavioral activation and overconfidence, whereas defense invokes neural networks for behavioral inhibition, vigilant scanning, and hostile attributions; and that (4) people invest less in attack than defense, and attack often fails. Finally, we propose that (5) in intergroup conflict, out-group attack needs institutional arrangements that motivate and coordinate collective action, whereas in-group defense benefits from endogenously emerging in-group identification. We discuss how games of attack and defense may have shaped human capacities for prosociality and aggression, and how third parties can regulate such conflicts and reduce their waste.

The various behavioral disciplines model human behavior in distinct and incompatible ways. Yet, recent theoretical and empirical developments have created the conditions for rendering coherent the areas of overlap of the various behavioral disciplines. The analytical tools deployed in this task incorporate core principles from several behavioral disciplines. The proposed framework recognizes evolutionary theory, covering both genetic and cultural evolution, as the integrating principle of behavioral science. Moreover, if decision theory and game theory are broadened to encompass other-regarding preferences, they become capable of modeling all aspects of decision making, including those normally considered “psychological,” “sociological,” or “anthropological.” The mind as a decision-making organ then becomes the organizing principle of psychology.

To understand the thinking process in private information games, we use \"Mousetracking\" to record which payoffs subjects attend to. The games have three information states and vary in strategic complexity. Subjects consistently deviate from Nash equilibrium choices and often fail to look at payoffs which they need to in order to compute an equilibrium response. Choices and lookups are similar when stakes are higher. When cluster analysis is used to group subjects according to lookup patterns and choices, three clusters appear to correspond approximately to level-3, level-2, and level-1 thinking in level-k models, and a fourth cluster is consistent with inferential mistakes (as, for example, in QRE or Cursed Equilibrium theories). Deviations from Nash play are associated with failure to look at the necessary payoffs. The time durations of looking at key payoffs can predict choices, to some extent, at the individual level and at the trial-by-trial level.

Backward induction is a widely accepted principle for predicting behavior in sequential games. In the classic example of the \"centipede game,\" however, players frequently violate this principle. An alternative is a \"dynamic level- k \" model, where players choose a rule from a rule hierarchy. The rule hierarchy is iteratively defined such that the level- k rule is a best response to the level- (k-1) rule, and the level- ∞ rule corresponds to backward induction. Players choose rules based on their best guesses of others' rules and use historical plays to improve their guesses. The model captures two systematic violations of backward induction in centipede games, limited induction and repetition unraveling. Because the dynamic level- k model always converges to backward induction over repetition, the former can be considered to be a tracing procedure for the latter. We also examine the generalizability of the dynamic level- k model by applying it to explain systematic violations of backward induction in sequential bargaining games. We show that the same model is capable of capturing these violations in two separate bargaining experiments. This paper was accepted by Peter Wakker, decision analysis.

We investigate the external validity of giving in the dictator game by using the misdirected letter technique in a within-subject design. First, subjects participated in standard dictator games (double blind) conducted in labs in two different studies. Second, after four to five weeks (study 1) or two years (study 2), we delivered prepared letters to the same subjects. The envelopes and the contents of the letters were designed to create the impression that they were misdirected by the mail delivery service. The letters contained 10 Euros (20 Swiss Francs in study 2) corresponding to the endowment of the in-lab experiments. We observe in both studies that subjects who showed other-regarding behavior in the lab returned the misdirected letters more often than subjects giving nothing, suggesting that in-lab behavior is related to behavior in the field.

This paper proposes a structural nonequilibrium model of initial responses to incomplete-information games based on \"level-k\" thinking, which describes behavior in many experiments with complete-information games. We derive the model's implications in first- and second-price auctions with general information structures, compare them to equilibrium and Eyster and Rabin's (2005) \"cursed equilibrium,\" and evaluate the model's potential to explain nonequilibrium bidding in auction experiments. The level-k model generalizes many insights from equilibrium auction theory. It allows a unified explanation of the winner's curse in common-value auctions and overbidding in those independent-private-value auctions without the uniform value distributions used in most experiments.

The level-k literature classifies subjects into different Lk types by their observed levels of reasoning in games. However, it remains unclear whether the observed level-k behavior is determined by belief or reasoning ability. This study proposes a strategy to identify the ability-bounded Lk subjects, who could not reason more than k steps of iterated best responses and thus have reached the upper bounds of their reasoning capacity. The identification utilizes a combination of simultaneous and sequential ring games. In the sequential games, it requires an extra step to best respond as Lk , and thus the ability-bounded ones would fail the task. Results show that more than half of the L 2 and L 3 subjects are ability-bounded. Additionally, subjects’ CRT scores, a measure of their cognitive ability, support the separation of the ability-bounded types. The findings suggest that both belief and reasoning ability could determine the observed levels, and thus one must be cautious when trying to infer belief or ability from the existing level-k data.

Research on small repeated decisions from experience suggests that people often behave as if they underweight rare events and choose the options that are frequently better. In a pandemic, this tendency implies complacency and reckless behavior. Furthermore, behavioral contagion exacerbates this problem. In two pre-registered experiments (Ntotal = 312), we validate these predictions and highlight a potential solution. Groups of participants played a repeated game in one of two versions. In the basic version, people clearly preferred the dangerous reckless behavior that was better most of the time over the safer responsible behavior. In the augmented version, we gave participants an additional alternative abstracting the use of an application that frequently saves time but can sometimes have high costs. This alternative was stochastically dominated by the responsible choice option and was thus normatively irrelevant to the decision participants made. Nevertheless, most participants chose the new (“irrelevant”) alternative, providing the first clear demonstration of underweighting of rare events in fully described social games. We discuss public policies that can make the responsible use of health applications better most of the time, thus helping them get traction despite being voluntary. In one field demonstration of this idea amid the COVID-19 pandemic, usage rates of a contact tracing application among nursing home employees more than tripled when using the app also started saving them a little time each day, and the high usage rates sustained over at least four weeks.