Stochastic games with information lag

Two-player zero-sum stochastic games with finite state and action spaces are known to have undiscounted values. We study such games under the assumption that one or both players observe the actions of their opponent after some time-dependent delay. We develop criteria for the rate of growth of the delay such that a player subject to such an information lag can still guarantee himself in the undiscounted game as much as he could have with perfect monitoring. We also demonstrate that the player in the Big Match with the absorbing action subject to information lags that grows too rapidly will not be able to guarantee as much as he could have in the game with perfect monitoring.     

Reciprocal relationships and mechanism design

We study an incomplete information game in which players can coordinate their actions by contracting among themselves. We model this relationship as a reciprocal contracting procedure where each player has the ability to make commitments contingent on the other players' commitments. We differ from the rest of the literature on reciprocal contracting by assuming that punishments cannot be enforced in the event that cooperation breaks down. We fully characterize the outcomes that can be supported as perfect Bayesian equilibrium outcomes in such an environment. We use our characterization to show that the set of supportable outcomes with reciprocal contracting is larger than the set of outcomes available in a centralized mechanism design environment in which the mechanism designer is constrained by his inability to enforce punishments against non‐participants. The difference stems from the players' ability in our contracting game to convey partial information about their types at the time they offer contracts. We discuss the implications of our analysis for modelling collusion between multiple agents interacting with the same principal.     

Pricing Monitoring Uncertainty in Climate Policy

This article assesses the environmental and economic efficiency of three different approaches to treat monitoring uncertainty in climate policy, namely prescribing uncertainty, setting minimum certainty thresholds and pricing uncertainty through a discount. Our model of the behavior of profit-maximizing agents demonstrates that under the simplest set of assumptions the regulator has no interest in reducing monitoring uncertainty. However, in the presence of information asymmetry, monitoring uncertainty may hamper the economic and environmental performance of climate policy due to adverse selection. In a mandatory policy, prescribing a reasonable level of uncertainty is preferable if the regulator has enough information to determine this level. For voluntary mechanisms, such as carbon offsets, allowing agents to set their own monitoring uncertainty below a maximum threshold or discounting carbon revenues in proportion to monitoring uncertainty are the best approaches for the regulator to mitigate the negative effects of information asymmetry. These conclusions are much more pronounced when agents do not accrue revenues from their mitigation action, other than carbon. Our analysis of monitoring uncertainty under information asymmetry, which results in heterogeneity in the agents’ benefits from abatement, generalizes the classical trade-off between production efficiency and information rents.     

The value of information in monotone decision problems

We study the information preferences and information demand of decision-makers facing uncertainty. We focus on monotone decision problems in which the posterior beliefs induced by the decision-maker’s information can be ordered so that higher actions are chosen in response to higher signal realizations. We provide necessary and sufficient conditions for decision makers with different classes of payoff functions to prefer one information structure to another. We also provide conditions under which two decision-makers in a given class can be ranked in terms of their information demand. Applications and examples are given.     

Past experience of uncertainty affects risk aversion

In an experiment with more than 500 participants we study how past experience of uncertainty (imperfect knowledge of the state space) affects risk preferences. Participants in our experiment choose between a sure outcome and a lottery in 32 periods. All treatments are exactly identical in periods 17–32 but differ in periods 1–16. In the early periods of the risk treatment there is perfect information about the lottery; in the ambiguity Treatment participants perfectly know the outcome space but not the associated probabilities; in the unawareness treatment participants have imperfect knowledge about both outcomes and probabilities. We observe strong treatment effects on behavior in periods 17–32. In particular, participants who have been exposed to an environment with very imperfect knowledge of the state space subsequently choose lotteries with high (low) variance less (more) often compared to other participants. Estimating individual risk attitudes from choices in periods 17–32 we find that the distribution of risk attitude parameters across our treatments can be ranked in terms of first order stochastic dominance. Our results show how exposure to environments with different degrees of uncertainty can affect individuals’ subsequent risk-taking behavior.     

Misery loves company: Social regret and social interaction effects in choices under risk and uncertainty

Extensive field evidence shows individuals? decisions in settings involving uncertainty depend on their peers? decisions. One hypothesized cause of peer group effects is social interaction effects: an individual?s utility from an action is enhanced by others taking the same action. We employ a series of controlled laboratory experiments to study the causes of peer effects in choice under uncertainty. We find strong peer group effects in the laboratory. Our design allows us to rule out social learning, social norms, group affiliation, and complementarities as possible causes for the observed peer group effects, leaving social interaction effects as the likely cause. We use a combination of theory and empirical analysis to show that preferences including “social regret” are more consistent with the data than preferences including a taste for conformity. We observe spillover effects, as observing another?s choice of one risky gamble makes all risky gambles more likely to be chosen.     

THE POWER OF WHISPERS: A THEORY OF RUMOR,COMMUNICATION, AND REVOLUTION*

We study how rumors mobilize individuals who take collective action. Rumors may or may not be informative, but they create public topics on which people can exchange their views. Individuals with diverse private information rationally evaluate the informativeness of rumors about regime strength. A rumor against the regime can coordinate a larger mass of attackers if individuals can discuss its veracity than if they cannot. Communication can be so effective that a rumor can have an even greater impact on mobilization than when the same story is fully believed by everybody. However, an extreme rumor can backfire and discourage mobilization.     

Testable implications of subjective expected utility theory

I show that the predictive content of the hypothesis of subjective expected utility maximization critically depends on what the analyst knows about the details of the problem a particular decision maker faces. When the analyst does not know anything about the agent's payoffs or beliefs and can only observe the sequence of actions taken by the decision maker any arbitrary sequence of actions can be implemented as the choice of an agent that solves some intertemporal utility maximization problem under uncertainty.     

Social welfare for an economy of angelic agents

This paper analyzes an economy in which all agents are pursuing the common good (or social welfare) but choices are decentralized, i.e., each agent can choose his/her action in the set of the actions that he/she can perform. One wonders if it is enough the common goal of maximizing social welfare to their will be achieved. The paper examines both the cases in which the choice made by each agent does not directly influence those of other agents, as in the competitive equilibrium analysis, and the case in which there is a direct influence, as in the game theory analyses. In the first case, we get that the common goal of maximizing social welfare is not enough to reach it, but it is necessary to coordinate the actions of individual agents by extending information to redistribute initial endowments and by introducing an appropriate social organization. We get the maximum social welfare without further intervention for the cases describable with the theory of games, but only for games of complete information. If the information is incomplete, some further coordination is generally required.     

INCOMPLETE INFORMATION GAMES WITH MULTIPLE PRIORS*

We present a model of incomplete information games, where each player is endowed with a set of priors. Upon arrival of private information, it is assumed that each player “updates” his set of priors to a set of posterior beliefs, and then evaluates his actions by the most pessimistic posterior beliefs. So each player's preferences may exhibit aversion to ambiguity or uncertainty. We define a couple of equilibrium concepts, establish existence results for them, and demonstrate by examples how players’ views on uncertainty about the environment affect the strategic outcomes.     

Learning from private information in noisy repeated games

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games where players observe imperfect public signals of the actions played, and both the payoff functions and the map from actions to signal distributions depend on an unknown state. The PTXE payoffs when players are patient are determined by the solutions to a family of linear programming problems. Using this characterization, we develop conditions under which play can be as if the players have learned the state. We provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.     

CRIME AND EDUCATION IN A MODEL OF INFORMATION TRANSMISSION

We model the decisions of young individuals to stay in school or drop out and engage in criminal activities. We build on the literature on human capital and crime engagement and use the framework of Banerjee (1993) that assumes that the information needed to engage in crime arrives in the form of a rumour and that individuals update their beliefs about the profitability of crime relative to education. These assumptions allow us to study the effect of social interactions on crime. In our model, we investigate informational spillovers from the actions of talented students to less talented students. We show that policies that decrease the cost of education for talented students may increase the vulnerability of less talented students to crime. The effect is exacerbated when students do not fully understand the underlying learning dynamics.     

DISPLAYING UNCERTAIN INFORMATION ABOUT PROBABILITY: EXPERIMENTAL EVIDENCE

Different from previous experiments that used three representations of uncertain information for probabilities: best estimate, interval and sets of probabilities, we use visual display to represent different levels of uncertainty through varying amount of probabilistic information provided to subjects. Results confirm that the individuals’ willingness to pay is higher when a larger amount of information is available. Further, individuals are found uncertainty averse for high probability of gain and uncertainty seekers for low probability of gain. Similarities in results across different representations of uncertainty indicate that the representation tested here is a viable method for communicating uncertainty to decision makers.     

Moral Hazard and Renegotiation with Multiple Agents

We investigate the effects of contract renegotiation in multi-agentsituations where risk-averse agents negotiate a contract offer to theprincipal after the agents observe a common, unverifiable perfect signalabout their actions. We show that renegotiation with multiple agentsreduces the cost of implementing any implementable action profile downto the first-best level, even though the principal cannot observe theagents' actions. Moreover, it is sufficient for the principal to use a"simple" initial contract, in the sense that it consists of nomore than a single sharing scheme for each agent and the total payments tothe agents are the same regardless of the realised state. An importantimplication is that decentralization, in the sense of delegated negotiationand proposals from the agents, can be as effective as centralized schemesthat utilize revelation mechanisms in unrestricted ways.     

Contagion and efficiency

We consider a population of agents, either finite or countably infinite, located on an arbitrary network. Agents interact directly only with their immediate neighbors, but are able to observe the behavior of (some) other agents beyond their interaction neighborhood, and learn from that behavior by imitating successful actions. If interactions are not “too global” but information is fluid enough, we show that the efficient action is the only one which can spread contagiously to the whole population from an initially small, finite subgroup. This result holds even in the presence of an alternative, -dominant action.     

Bayesian learning in social networks

We extend the standard model of social learning in two ways. First, we introduce a social network and assume that agents can only observe the actions of agents to whom they are connected by this network. Secondly, we allow agents to choose a different action at each date. If the network satisfies a connectedness assumption, the initial diversity resulting from diverse private information is eventually replaced by uniformity of actions, though not necessarily of beliefs, in finite time with probability one. We look at particular networks to illustrate the impact of network architecture on speed of convergence and the optimality of absorbing states. Convergence is remarkably rapid, so that asymptotic results are a good approximation even in the medium run.     

Self-serving altruism? The lure of unethical actions that benefit others

In three experiments, we propose and find that individuals cheat more when others can benefit from their cheating and when the number of beneficiaries of wrongdoing increases. Our results indicate that people use moral flexibility to justify their self-interested actions when such actions benefit others in addition to the self. Namely, our findings suggest that when people's dishonesty would benefit others, they are more likely to view dishonesty as morally acceptable and thus feel less guilty about benefiting from cheating. We discuss the implications of these results for collaborations in the social realm.     

Banning Bidders from All-pay Auctions

We consider an all-pay auction with complete information among the bidders; the seller does not observe the bidders’ values. We show that for some information structures in which the seller has a small uncertainty about the valuations, it is profitable for him to exclude from the auction all but two (randomly selected) bidders even though the latter are ex ante identical from his point of view.I am grateful to Paolo Bertoletti who introduced me to this topic and provided useful comments. I also thank Dan Kovenock (Co-Editor) and two anonymous referees for suggestions which considerably improved the exposition.     

Age- and health-related non-linear inheritance taxation

This paper studies the design of optimal non linear bequest taxation when individuals differ in wage, survival and probability to become dependent at the old age. Following the recent health and economic literature, we assume that agents with higher wage have higher survival chances and lower risks to become dependent. Agents make precautionary savings for their old age taking into account the uncertainty on their health. They exhibit joy of giving utility, so that they also set aside money for their heirs. In the absence of annuity and long-term care (LTC) insurance markets, heirs obtain different levels of bequests, depending on whether the donor died early or late in life and whether he was healthy at time of death. We assume that the government does not observe the decomposition of bequests between voluntary and involuntary ones. Instead, it observes the timing of death and the health condition at death of the donor. We show that, under asymmetric information, on top of marginal income taxation, the bequests left by low-income individuals in case of early death should be taxed at the margin. To the opposite, bequests obtained later in life need not be taxed or subsidized at the margin.     

The importance of higher-order beliefs to successful coordination

Beliefs about other players’ strategies are crucial in determining outcomes for coordination games. If players are to coordinate on an efficient equilibrium, they must believe that others will coordinate with them. In many settings there is uncertainty about beliefs as well as strategies. Do people consider these “higher-order” beliefs (beliefs about beliefs) when making coordination decisions? I design a modified stag hunt experiment that allows me to identify how these higher-order beliefs and uncertainty about higher-order beliefs matter for coordination. Players prefer to invest especially when they believe that others are “optimistic” that they will invest; but knowledge that others think them unlikely to invest does not cause players to behave differently than when they do not know what their partners think about them. Thus resolving uncertainty about beliefs can result in marked efficiency gains.