The Cry Wolf Effect in Evacuation: a Game-Theoretic Approach

In today's terrorism-prone and security-focused world, evacuation emergencies, drills, and false alarms are becoming more and more common. Compliance to an evacuation order made by an authority in case of emergency can play a key role in the outcome of an emergency. In case an evacuee experiences repeated emergency scenarios which may be a false alarm (e.g., an evacuation drill, a false bomb threat, etc.) or an actual threat, the Aesop's cry wolf effect (repeated false alarms decrease order compliance) can severely affect his/her likelihood to evacuate. To analyse this key unsolved issue of evacuation research, a game-theoretic approach is proposed. Game theory is used to explore mutual best responses of an evacuee and an authority. In the proposed model the authority obtains a signal of whether there is a threat or not and decides whether to order an evacuation or not. The evacuee, after receiving an evacuation order, subsequently decides whether to stay or leave based on posterior beliefs that have been updated in response to the authority's action. Best-responses are derived and Sequential equilibrium and Perfect Bayesian Equilibrium are used as solution concepts (refining equilibria with the intuitive criterion). Model results highlight the benefits of announced evacuation drills and suggest that improving the accuracy of threat detection can prevent large inefficiencies associated with the cry wolf effect.Comment: To be published in Physica

Assortativity evolving from social dilemmas

Assortative mechanisms can overcome tragedies of the commons that otherwise result in dilemma situations. Assortativity criteria include genetics (e.g. kin selection), preferences (e.g. homophily), locations (e.g. spatial interaction) and actions (e.g. meritocracy), usually presuming an exogenously fixed matching mechanism. Here, we endogenize the matching process with the aim of investigating how assortativity itself, jointly with cooperation, is driven by evolution. Our main finding is that only full-or-null assortativities turn out to be long-run stable, their relative stabilities depending on the exact incentive structure of the underlying social dilemma. The resulting social loss is evaluated for general classes of dilemma games, thus quantifying to what extent tragedy of the commons may be endogenously overcome

Emergence of specialized third-party enforcement

The question of how cooperation evolves and is maintained among nonkin is central to the biological, social, and behavioral sciences. Previous research has focused on explaining how cooperation in social dilemmas can be maintained by direct and indirect reciprocity among the participants of the social dilemma. However, in complex human societies, both modern and ancient, cooperation is frequently maintained by means of specialized third-party enforcement. We provide an evolutionary-game-theoretic model that explains how specialized third-party enforcement of cooperation (specialized reciprocity) can emerge. A population consists of producers and enforcers. First, producers engage in a joint undertaking represented by a prisoner’s dilemma. They are paired randomly and receive no information about their partner’s history, which precludes direct and indirect reciprocity. Then, enforcers tax producers and may punish their clients. Finally, the enforcers are randomly paired and may try to grab resources from each other. In order to sustain producer cooperation, enforcers must punish defecting producers, but punishing is costly to enforcers. We show that the threat of potential intraenforcer conflict can incentivize enforcers to engage in costly punishment of producers, provided they are sufficiently informed to maintain a reputation system. That is, the “guards” are guarded by the guards themselves. We demonstrate the key mechanisms analytically and corroborate our results with numerical simulations

The normality assumption in coordination games with flexible information acquisition

Many economic models assume that random variables follow normal (Gaussian) distributions. Yet, real-world variables may be non-normally distributed. How sensitive are these models' predictions to distribution misspecifications? This paper addresses the question in the context of linear-quadratic beauty contests played by rationally inattentive players. It breaks with the assumption that the (common prior) distribution of the fundamental be Gaussian and provides a characterization of the class of equilibria in continuous strategies. The characterization is used to show that small departures from normality can lead to distributions of the equilibrium average action that are qualitatively different from those of Gaussian models. Numerical results show that the rate at which an analyst's errors in determining the fundamental's distribution are amplified in her prediction is higher when the true prior is non-Gaussian than when it is an equally-misspecified Gaussian

Flexible Information Acquisition in Large Coordination Games

This paper studies how large populations of rationally inattentive individuals acquire information about economic fundamentals when, along with the motive to accurately estimate the fundamental, they have coordination motives. Information acquisition is costly but flexible: players determine the distribution of the signal that they receive and arbitrarily correlate it with the fundamental, paying costs linear in Shannon mutual information. Without assuming a normal prior for the fundamental, the class of equilibria in continuous strategies is characterized. Populations with heterogeneous costs exhibit the same aggregate behavior as homogeneous populations with the same average cost. Equilibria where the population-wide average action is an affine function of the fundamental exist only when the fundamental is normally distributed. Finally, a novel method allows to study non-normal priors, leading to new insights. For example, the distribution of the equilibrium action exhibits an amplified skewness compared to the distribution of the fundamental

Essays in Game Theory

This thesis explores interactions among agents whose rationality is bounded in distinct ways. It consists of three self-contained chapters/papers. Chapters 2 and 3 consider myopic and hard-wired strategy revisions based on evolutionary game dynamics, while Chapter 4 deals with rationally inattentive agents who acquire costly information in a flexible manner. The thesis, thus, spans two extremes of the range of models with boundedly rational agents. The first paper proposes a novel way to formalize matching mechanisms in evolutionary games. The proposed formalization nests group selection models such as the haystack (Maynard Smith, 1964) and trait-group models (Wilson, 1975). It is shown that evolutionary optima can be obtained as Nash equilibria under appropriately defined matching rules. In the second paper matching rules are endogenized and the co-evolution of cooperation and matching is studied in social dilemma situations. It turns out that only full-or-null assortativity levels are evolutionarily stable. The extent to which efficient outcomes are achieved by this endogenization process is evaluated, which crucially depends on the structure of the particular interaction considered. The third paper extends recent models of flexible information acquisition to an uncountable-action-space setting: a beauty contest coordination game. Necessary conditions for the existence of equilibria with well-behaved strategies are derived. It is established that affine equilibria exist only if the fundamental is normally distributed. A higher coordination motive, a more concentrated prior distribution of the fundamental and higher information costs lead to less attention being paid to the fundamental. Moreover, flexible information acquisition technology is shown to result in equilibrium multiplicity under certain parameter combinations

Discontinuous and continuous stochastic choice and coordination in the lab

We experimentally test theoretical predictions on equilibrium selection in a two-player coordination (investment) game. Through a minimal visual variation, our design prompts participants to play strategies whereby investing probability is either continuous or discontinuous in the payoff-relevant state. When participants use continuous strategies, average behavior is consistent with play in the risk-dominant equilibrium, the unique theoretical prediction. When they use discontinuous strategies, average behavior is closer to the payoff-dominant equilibrium strategy. In this case, the theory predicts multiple equilibria, for which we find no support. Additionally, we extend the theory to heterogeneous populations: the set of equilibria monotonically decreases in the proportion of players who use continuous strategies

Discontinuous and Continuous Stochastic Choice and Coordination in the Lab

Coordination games have multiple equilibria under complete information. However, recent theoretical advances show that if players are uncertain but can acquire information about a payoff-relevant state of the world, the number of equilibria depends on whether they can implement strategies (stochastic choice rules) discontinuous in the state. We experimentally test these results in a two-player investment game. Through a minimal visual variation in the design (our treatment) we prompt participants to play strategies whereby their probability to invest is either continuous or discontinuous in the payoff-relevant state. When participants use continuous strategies, average behavior is consistent with play in the risk-dominant equilibrium, the unique theoretical prediction. When they use discontinuous strategies—in¬¬ which case there are multiple equilibria—average behavior is closer to the payoff-dominant equilibrium strategy. Additionally, we extend the theory to heterogeneous populations: the set of equilibria monotonically decreases in the proportion of players who use continuous strategies

Assortativity evolving from social dilemmas

Assortative mechanisms can overcome tragedies of the commons that otherwise result in dilemma situations. Assortativity criteria include various forms of kin selection, greenbeard genes, and reciprocal behaviors, usually presuming an exogenously fixed matching mechanism. Here, we endogenize the matching process with the aim of investigating how assortativity itself, jointly with cooperation, is driven by evolution. Our main finding is that full-or-null assortativities turn out to be long-run stable in most cases, independent of the relative speeds of both processes. The exact incentive structure of the underlying social dilemma matters crucially. The resulting social loss is evaluated for general classes of dilemma games, thus quantifying to what extent the tragedy of the commons may be endogenously overcome