Pairwise interact-and-imitate dynamics

This paper introduces and studies a class of evolutionary dynamics—pairwise interact-and-imitate dynamics (PIID)—in which agents are matched in pairs, engage in a symmetric game, and imitate the opponent with a probability that depends on the difference in their payoffs. We provide a condition on the underlying game, named supremacy, and show that the population state in which all agents play the supreme strategy is globally asymptotically stable. We extend the framework to allow for payoff uncertainty, and check the robustness of our results to the introduction of some heterogeneity in the revision protocol followed by agents. Finally, we show that PIID can allow the survival of strictly dominated strategies, leads to the emergence of inefficient conventions in social dilemmas, and makes assortment ineffective in promoting cooperation.

Pairwise Interact-and-Imitate Dynamics

This paper introduces and studies a class of evolutionary dynamics --- Pairwise Interact-and-Imitate Dynamics (PIID) --- in which agents are matched in pairs, engage in a symmetric game, and imitate the opponent with a probability that depends on the difference in their payoffs. We provide a condition on the underlying game, named supremacy, and show that the population state in which all agents play the supreme strategy is globally asymptotically stable. We extend the framework to allow for payoff uncertainty, and check the robustness of our results to the introduction of some heterogeneity in the revision protocol followed by agents. Finally, we show that PIID can allow the survival of strictly dominated strategies, leads to the emergence of inefficient conventions in social dilemmas, and makes assortment ineffective in promoting cooperation.

Contracting under uncertainty: Groundwater in South India

To quantify contracting distortions in a real‐world market, we develop and structurally estimate a model of contracting under payoff uncertainty in the south Indian groundwater economy. Uncertainty arises from unpredictable fluctuations in groundwater supply during the agricultural dry season. Our model highlights the tradeoff between the ex post inefficiency of long‐term contracts and the ex ante inefficiency of spot contracts. We use unique data on both payoff uncertainty and relationship‐specific investment collected from a large sample of well‐owners in Andhra Pradesh to estimate the model's parameters. Our estimates imply that spot contracts entail a 3% efficiency loss due to hold‐up. Counterfactual simulations also reveal that the equilibrium contracting distortion reduces the overall gains from trade by about 4% and the seasonal income of the median borewell owner by 2%, with proportionally greater costs borne by smaller landowners.

Refinements and higher-order beliefs: a unified survey

This paper presents a simple framework that allows us to survey and relate some different strands of the game theory literature. We describe a “canonical” way of adding incomplete information to a complete information game. This framework allows us to give a simple “complete theory” interpretation (Kreps in Game theory and economic modelling. Clarendon Press, Oxford, 1990) of standard normal form refinements such as perfection, and to relate refinements both to the “higher-order beliefs literature” (Rubinstein in Am Econ Rev 79:385–391, 1989; Monderer and Samet in Games Econ Behav 1:170–190, 1989; Morris et al. in Econ J Econ Soc 63:145–157, 1995; Kajii and Morris in Econ J Econ Soc 65:1283–1309, 1997a) and the “payoff uncertainty approach” (Fudenberg et al. in J Econ Theory 44:354–380, 1988; Dekel and Fudenberg in J Econ Theory 52:243–267, 1990).

Collective Action with Uncertain Payoffs: Coordination, Public Signals, and Punishment Dilemmas

How can one analyze collective action in protests or revolutions when individuals are uncertain about the relative payoffs of the status quo and revolution? We model a “calculus of protest” of individuals who must either submit to the status quo or support revolt based only on personal information about their payoffs. In deciding whether to revolt, the citizen must infer both the benefit of successful revolution and the likely actions of other citizens. We characterize conditions under which payoff uncertainty overturns conventional wisdom: (a) when a citizen is too willing to revolt, he reduces the incentives of others to revolt; (b) less accurate information about the value of revolution can make revolt more likely; (c) public signals from other citizens can reduce the likelihood of revolt; (d) harsher punishment can increase the incidence of punishment; and (e) the incidence of protest can be positively correlated with that of repression.