Murali Agastya

Adaptive Play in Multiplayer Bargaining Situations

We study the dual issues of allocation and coalition formation in a model of social learning. For a class of economies which can be expressed in terms of a real valued characteristic function, we first show that all self-perpetuating allocations realized from a simple bargaining game must be core allocations although players make simultaneous demands for surplus and only on their own behalf. Following this, we provide a sufficient condition under which the society eventually learns to divide the surplus according to some core allocation, regardless of the initial history.

Stochastic Stability in a Double Auction

In a k-double auction, a buyer and a seller must simultaneously announce a bid and an ask price respectively. Exchange of the indivisible good takes place if and only if the bid is at least as high as the ask, the trading price being the bid price with probability k and the ask price with probability (1 - k). We show that the stable equilibria of a complete information k-double approximate an asymmetric Nash Bargaining solution with the sellers bargaining power decreasing in k. Note that ceteras paribus, the payoffs of the seller of the one-shot game increase in k. Nevertheless, as the stochastically stable equilibrium price decreases in k, choosing the sellers favourite price with a relatively higher probability in individual encounters makes him worse off in the long run.

On Choice in Complex Environments

A Decision Maker (DM) must choose at discrete moments from a finite set of actions that result in random rewards. The environment is complex in that she finds it impossible to describe the states and is thus prevented from application of standard Bayesian methods. This paper presents an axiomatic theory of choice in such environments. Our approach is to postulate that the DM has a preference relation defined directly over the set of actions which is updated over time in response to the observed rewards. Three simple axioms that highlight the independence of the given actions, the bounded rationality of the agent, and the principle of insufficient reason at margin are necessary and sufficient for the DMs preferences to admit a utility representation. The DMs behavior in this case will be akin to fictitious play. We then show that, if rewards are drawn by a stationary stochastic process, the observed behavior of such a DM almost surely cannot be distinguished from anyone who is fully cognizant of the environment.

Insider Trading, Informational Effciency and Allocative Effciency

A dominant, net buyer of a certain asset receives a private signal that is correlated with its mean value. We call this insider a Boesky Insider when the quality of the received signal is such that the future value of the asset can be predicted with certainty. We show that even an infinitesimal probability of a Boesky Insider results in informational inefficiency of prices. Insisting that the equilibrium be continuous in the signal accentuates the inefficiency to the extent that no information is conveyed. The informational inefficiency not withstanding, the regime that allows insider trading can result in greater liquidity and is, in an ex-ante sense, Pareto superior when compared to a regime in which insider trading is banned.

Task Ordering in Incentives Under Externalities

In a two-task team project with observable task outcomes, optimal incentives prioritize tasks differently depending on task externalities. When the tasks are independent, Principal follows a decreasing order by placing more essential task first. A task is more essential if its failure compromises the overall projects chance of success from a task-specific cutoff level by a greater percentage. This definition has no systematic relations to the variance of task outcomes. In particular, a more risky task can be less essential or more essential. Under externalities, essentiality and impact jointly determine the optimal ordering. A task with much higher impact can be performed early even if it is less essential. Optimal task ordering thus raises subtle new issues and forms an integral part in team incentives. Our analysis provides some contrast with recent team incentives results.

Rank Order Solutions for Coalition Form Games

This paper advances the idea that, in a variety of environments, it is natural to think of the solution of a (coalition form) game as an ordering of the players rather than as a division of the value of coalitions. Orderings that are characterized by an average of the desirability of one player to another across coalitions are axiomatized. This includes the rule where i is ranked above j if and only if the Shapley Value of i in the game without j is greater than the Shapley Value of j in the game without i. The result is applicable to arbitration schemes, scheduling problems, etc.

On Choosing which Game to Play when Ignorant of the Rules

This paper suggests a theory of choice among strategic situations when the rules of play are not properly specified. We take the view that a “strategic situation” is adequately described by a TU game since it specifies what is feasible for each coalition but is silent on the procedures that are used to allocate the surplus. We model the choice problem facing a decision maker (DM) as having to choose from finitely many “actions”. The known “consequence” of the ith action is a coalition from game f i over a fixed set of players \(N_i\cup\{d\}\) (where d stands for the DM). Axioms are imposed on her choice as the list of consequences (f 1,..., f m ) from the m actions varies. We characterize choice rules that are based on marginal contributions of the DM in general and on the Shapley Value in particular.

Incentive Compatibility: Everywhere vs. Almost Everywhere

A risk neutral buyer observes a private signal s 2 [a,b], which informs her that the mean and variance of a normally distributed risky asset are s and 2 s respectively. She then sets a price at which to acquire the asset owned by risk averse “outsiders”. Assume 2 s 2 0, 2 for some 2 > 0 and let B = s 2 [a,b] | 2 = 0 . If B = ;, then there exists a fully revealing equilibrium in which trade occurs. If B 6 ;, no such equilibrium can exist, even if B is of measure zero.

A Note on Risk Aversion and Evolution to Equilibrium in 2x2 Coordination Games

In this note we point out the effect of risk-aversion on both the speed of deterministic convergence and the waiting times involved in equilibrium selection in 2 X 2 coordination games. Risk-aversion destabilizes the Pareto optimal equilibrium in two different ways: it decreases the size of its basin of attraction and slows the rate of deterministic convergence within its basin of attraction. It turns out that the first effect is quite significant: moderate levels of risk aversion are enough even in large populations to lead the system from the Pareto Optimal equilibrium to a risk-dominant equilibrium after just one mutation.

Extremes and Moderates: A Characterization and an Application to Lobbying

Abstract: In a society where individuals differ in their valuation of different social policies, when might one consider a given individual as having references that are extreme relative to the others? And how important are such preferences in determining eventual policy? In this paper, we describe an individual as being extreme if her views differ from the mainstream to the extent that the rest of the society is able to unanimously agree on a compromise policy that they strictly prefer to what might have been the outcome if such an individual has her own way. Relying on the intermediate property of preferences due to Grandmont [1978] we provide a simple geometric characterization of extreme preferences. Furthermore, we also present an illustrative positive model of lobbying activity where we apply our characterization result to show that every equilibrium social policy is determined only by the activities of those holding extreme preferences even when they are a minority