Rajiv Sarin

Continuous Approximations of Stochastic Evolutionary Game Dynamics

Continuous approximations that are ordinary differential equations (ODEs) or stochastic differential equations (SDEs) are often used to study the properties of discrete stochastic processes. We show that different ways of taking the continuous limit of the same model may result in either an ODE or a SDE and study the manner in which each approximates the discrete model. We compare the asymptotic properties of the continuous equations with those of the discrete dynamics and show that they tend to provide a better approximation when a greater amount of variance of the discrete model is preserved in the continuous limit. Journal of Economic Literature Classification numbers: C6, C7, D8

Is Reputation Good or Bad? An Experiment

We investigate the impact of reputation in a laboratory experiment. We do so by varying whether the past choices of a long-run player are observable by the short-run players. Our framework allows for reputation to have either a beneficial or a harmful effect on the long-run player. We find that reputation is seldom harmful and its beneficial effects are not as strong as theory suggests. When reputational concerns are at odds with other-regarding preferences, we find th latter overwhelm the former. (JEL C91, D12, D82, D83, Z13)

STRATEGY SIMILARITY AND COORDINATION

An anti-smog filtration system receives exhaust gases from a burning device and passes them through a chemical solution for separating the particulates into the solution. The remaining exhaust gases are recirculated for further separation of particulates into the solution and exhausted. The impregnated solution is passed through a mechanical filtration tank for removal of particulates therefrom and the remainder going to drain.

Players With Limited Memory

This paper studies a model of memory. The model takes into account that memory capacity is limited and imperfect. We study how agents with such memory limitations, who have very little information about their choice environment, play games. We introduce the notion of a Limited Memory Equilibrium (LME) and show that play converges to an LME in every generic normal form game. Our characterization of the set of LME suggests that players with limited memory do (weakly) better in games than in decision problems. We also show that agents can do quite well even with severely limited memory, although severe limitations tend to make them behave cautiously.

Decision Rules with Bounded Memory

Abstract We study a model in which a decision maker has limited memory. For a large class of decision rules that may be used to select among strategies, the decision maker converges to play the maxmin strategy. The result arises not because of any inherent caution on the part of the decision maker, but because the decision makers memory eventually contains only bad payoffs from the strategies no longer considered the best. Hence, a new rationale is provided for maxmin behavior. Journal of Economic Literature Classification Numbers : C72, D83.

Simple play in the Prisoner’s Dilemma ☆

Abstract Players do not have knowledge of the objective game. They know the available strategies and have scalar valued non-probabilistic payoff assessments. They act myopically, always choosing the strategy they consider best. They update these assessments in the direction of the received payoff. It is shown that such players converge to choose their maxmin strategies when facing a game against nature. In the Prisoner’s Dilemma, however, the players need not converge to their maxmin strategy, and often end up cooperating.

Learning and risk aversion

We study how learning shapes behavior towards risk when individuals are not assumed to know, or to have beliefs about, probability distributions. In any period, the behavior change induced by learning is assumed to depend on the action chosen and the payoff obtained. We characterize learning processes that, in expected value, increase the probability of choosing the safest actions and provide sufficient conditions for them to converge to the choices of risk averse expected utility maximizers. We provide a learning theoretic motivation for long run risk choices, such as those in expected utility theory with known payoff distributions.

Two-Stage Buy-It-Now Auctions

This paper studies second-price auctions with a temporary Buy-It-Now price (BIN auctions) using a two-stage model, in which two groups of bidders enter the auction at different times. The early bidders are offered a Buy-It-Now (BIN) option to purchase the item immediately at a listed price (BIN price). If no early bidder accepts the BIN option, an additional group of bidders (late bidders) enter the auction and both groups of bidders participate in a second-price sealed-bid auction without BIN option. When bidders are risk averse with concave utility functions, we establish the existence and uniqueness of a cutoff equilibrium such that an early bidder will accept the BIN option if his valuation is higher than the cutoff valuation. Moreover, bidders are more likely to accept the BIN option when fewer bidders are offered the BIN option. We show that when facing risk averse bidders, the seller can obtain higher expected revenue in BIN auctions than in standard second-price auctions. Furthermore, the expected seller revenue decreases with the number of early bidders. Consequently, the expected seller revenue is higher in the auctions with BIN only available to a subset of bidders than in the auctions with BIN available to all bidders. These results may help explain the popularity of temporary BIN auctions on eBay and the observed high acceptance frequencies of BIN prices in experimental and field studies.

An experiment on first-price common-value auctions with asymmetric information structures: The blessed winner

In common-value auctions bidders have access to public information, and may also hold private information prior to choosing their bids. The literature has predominately focused on the case in which bidders are ex-ante symmetric and privately informed, and finds that aggressive bidding such that payoffs are negative is common (the winners curse). In practice, bidders often only have access to public information, and use this information to form (possibly differing) beliefs. In addition, a bidder who is not privately informed may face bidders who are. We examine bidding behavior of both informed and uninformed bidders, and vary the information structure they face. We find that uninformed bidders underbid dramatically and persistently, while informed bidders tend to overbid in the two-bidder case. Our results highlight the importance of correctly modeling the information available to bidders.

Mean and variance responsive learning

Decision makers are often described as seeking higher expected payoffs and avoiding higher variance in payoffs. We provide some necessary and some sufficient conditions for learning rules, that assume the agent has little prior and feedback information about the environment, to reflect such preferences. We adopt the framework of Borgers, Morales and Sarin (2004, Econometrica) who provide similar results for learning rules that seek higher expected payoffs. Our analysis reveals that a concern for variance leads to quadratic transformations of payoffs to appear in the learning rule.