Three Essays on Dynamic Games
Three Essays on Dynamic Games

Author: Asaf Plan

Publisher:

Published: 2010

Total Pages: 70

ISBN-13:

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Chapter 1: This chapter considers a new class of dynamic, two-player games, where a stage game is continuously repeated but each player can only move at random times that she privately observes. A player's move is an adjustment of her action in the stage game, for example, a duopolist's change of price. Each move is perfectly observed by both players, but a foregone opportunity to move, like a choice to leave one's price unchanged, would not be directly observed by the other player. Some adjustments may be constrained in equilibrium by moral hazard, no matter how patient the players are. For example, a duopolist would not jump up to the monopoly price absent costly incentives. These incentives are provided by strategies that condition on the random waiting times between moves; punishing a player for moving slowly, lest she silently choose not to move. In contrast, if the players are patient enough to maintain the status quo, perhaps the monopoly price, then doing so does not require costly incentives. Deviation from the status quo would be perfectly observed, so punishment need not occur on the equilibrium path. Similarly, moves like jointly optimal price reductions do not require costly incentives. Again, the tempting deviation, to a larger price reduction, would be perfectly observed. This chapter provides a recursive framework for analyzing these games following Abreu, Pearce, and Stacchetti (1990) and the continuous time adaptation of Sannikov (2007). For a class of stage games with monotone public spillovers, like differentiated-product duopoly, I prove that optimal equilibria have three features corresponding to the discussion above: beginning at a "low" position, optimal, upward moves are impeded by moral hazard; beginning at a "high" position, optimal, downward moves are unimpeded by moral hazard; beginning at an intermediate position, optimally maintaining the status quo is similarly unimpeded. Corresponding cooperative dynamics are suggested in the older, non-game-theoretic literature on tacit collusion. Chapter 2: This chapter shows that in finite-horizon games of a certain class, small perturbations of the overall payoff function may yield large changes to unique equilibrium payoffs in periods far from the last. Such perturbations may tie together cooperation across periods in equilibrium, allowing substantial cooperation to accumulate in periods far from the last. Chapter 3: A dynamic choice problem faced by a time-inconsistent individual is typically modeled as a game played by a sequence of her temporal selves, solved by SPNE. It is recognized that this approach yields troublesomely many solutions for infinite-horizon problems, which is often attributed to the existence of implausible equilibria based on self-reward and punishment. This chapter presents a refinement applicable within the special class of strategically constant (SC) problems, which are those where all continuation problems are isomorphic. The refinement requires that each self's strategy be invariant, here that implies history-independence under the isomorphism. I argue that within the class of SC problems, this refinement does little more than rule out self-reward and punishment. The refinement substantially narrows down the set of equilibria in SC problems, but in some cases allows plausible equilibria that are excluded by other refinement approaches. The SC class is limited, but broader than it might seem at first.

Essays on Dynamic Games and Reputations
Essays on Dynamic Games and Reputations

Author: Di Pei (Ph. D.)

Publisher:

Published: 2018

Total Pages: 189

ISBN-13:

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This thesis consists of three essays on dynamic games with incomplete information. In Chapter 1, I study reputation effects when individuals have persistent private information that matters for their opponents' payoffs. I examine a repeated game between a patient informed player and a sequence of myopic uninformed players. The informed player privately observes a persistent state, and is either a strategic type who can flexibly choose his actions or is one of the several commitment types that mechanically plays the same action in every period. Unlike the canonical models on reputation effects, the uninformed players' payoffs depend on the state. This interdependence of values introduces new challenges to reputation building, namely, the informed player could face a tradeo between establishing a reputation for commitment and signaling favorable information about the state. My results address the predictions on the informed player's payoff and behavior that apply across all Nash equilibria. When the stage game payoffs satisfy a monotone-supermodularity condition, I show that the informed long-run player can overcome the lack-of-commitment problem and secure a high payoff in every state and in every equilibrium. Under a condition on the distribution over states, he will play the same action in every period and maintain his reputation for commitment in every equilibrium. If the payoff structure is unrestricted and the probability of commitment types is small, then the informed player's return to reputation building can be low and can provide a strict incentive to abandon his reputation. In Chapter 2, I study the dynamics of an agent's reputation for competence when the labor market's information about his performance is disclosed by an intermediary who cannot commit. I show that this game admits a unique Markov Perfect Equilibrium (MPE). When the agent is patient, his effort is inverse U-shaped, while the rate of information disclosure is decreasing over time. I illustrate the inefficiencies of the unique MPE by comparing it with the equilibrium in the benchmark scenario where the market automatically observes all breakthroughs. I characterize a tractable subclass of non-Markov Equilibria and explain why allowing players to coordinate on payoff-irrelevant events can improve eciency on top of the unique MPE and the exogenous information benchmark. When the intermediary can commit, her optimal Markov disclosure policy has a deadline, after which no breakthrough will be disclosed. However, deadlines are not incentive compatible in the game without commitment, illustrating a time inconsistency problem faced by the intermediary. My model can be applied to professional service industries, such as law and consulting. My results provide an explanation to the observed wage and promotion patterns in Baker, Gibbs and Holmström (1994). In Chapter 3, I study repeated games in which a patient long-run player (e.g. a rm) wishes to win the trust of some myopic opponents (e.g. a sequence or a continuum of consumers) but has a strict incentive to betray them. Her benet from betrayal is persistent over time and is her private information. I examine the extent to which persistent private information can overcome this lack-of-commitment problem. My main result characterizes the set of payoffs a patient long-run player can attain in equilibrium. Interestingly, every type's highest equilibrium payoff only depends on her true benet from betrayal and the lowest possible benet in the support of her opponents' prior belief. When this lowest possible benet vanishes, every type can approximately attain her Stackelberg commitment payoff. My finding provides a strategic foundation for the (mixed) Stackelberg commitment types in the reputation models, both in terms of the highest attainable payoff and in terms of the commitment behaviors. Compared to the existing approaches that rely on the existence of crazy types that are either irrational or have drastically dierent preferences, there is common knowledge of rationality in my model, and moreover, players' ordinal preferences over stage game outcomes are common knowledge.

Essays on Information in Dynamic Games and Mechanism Design
Essays on Information in Dynamic Games and Mechanism Design

Author: Daehyun Kim

Publisher:

Published: 2019

Total Pages: 153

ISBN-13:

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This dissertation studies how asymmetric information between economic agents interacts with their incentive in dynamic games and mechanism design. Chapter 1 and Chapter 2 study this in mechanism design, especially focusing on robustness of mechanisms when a mechanism designer's knowledge on agents' belief and higher order beliefs is not perfect. In Chapter 1 we introduce a novel robustness notion into mechanism design, which we term confident implementation; and characterize confidently implementable social choice correspondences. In Chapter 2, we introduce another robust notion, p-dominant implementation where p [0, 1]N and N N is the number of agents, and fully characterize p-dominant implementable allocations in the quasilinear environment. Chapter 1 and Chapter 2 are related in the following way: for some range of p, a p-dominant implementable social choice correspondence is confidently implementable. In Chapter 3, we study information disclosure problem to manage reputation. To study this, we consider a repeated game in which there are a long-run player and a stream of short-run players; and the long-run player has private information about her type, which is either commitment or normal. We assume that the shot-run player only can observe the past K N periods of information disclosed by the long-run player. In this environment, we characterize the information disclosure behavior of the long-run player and also equilibrium dynamics whose shape critically depends on the prior.