arXiv subjects
Publications and source records attributed to Srinivas Arigapudi.
We examine functions representing the cumulative probability of a binomial random variable exceeding a threshold, expressed in terms of the success probability per trial. These functions are known to exhibit a unique inflection point. We generalize this property to their compositions and highlight its applications.
Coordination games admit two types of equilibria: pure equilibria, where all players successfully coordinate their actions, and mixed equilibria, where players frequently experience miscoordination. The existing literature shows that under many evolutionary dynamics, populations converge to a pure equilibrium from almost any initial distribution of actions. By contrast, we show that under plausible learning dynamics, where agents observe the actions of a random sample of their opponents and adjust their strategies accordingly, stable miscoordination can arise when there is heterogeneity in the sample sizes. This occurs when some agents make decisions based on small samples (anecdotal evidence) while others rely on large samples. Finally, we demonstrate the empirical relevance of our results in a bargaining application. Final pre-print of a manuscript accepted for publication in American Economic Journal: Microeconomics.
We study games in which the set of strategies is multi-dimensional, and new agents might learn various strategic dimensions from different mentors. We introduce a new family of dynamics, the recombinator dynamics, which is characterised by a single parameter, the recombination rate r in [0,1]. The case of r = 0 coincides with the standard replicator dynamics. The opposite case of r = 1 corresponds to a setup in which each new agent learns each new strategic dimension from a different mentor, and combines these dimensions into her adopted strategy. We fully characterise stationary states and stable states under these dynamics, and we show that they predict novel behaviour in various applications.
The hawk-dove game admits two types of equilibria: an asymmetric pure equilibrium in which players in one population play hawk and players in the other population play dove, and an inefficient symmetric mixed equilibrium, in which hawks are frequently matched against each other. The existing literature shows that populations will converge to playing one of the pure equilibria from almost any initial state. By contrast, we show that plausible sampling dynamics, in which agents occasionally revise their actions by observing either opponents' behavior or payoffs in a few past interactions, can induce the opposite result: global convergence to one of the inefficient mixed stationary states.
We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner`s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature.