Cooperative Games with Overlapping Coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions--or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

Auctions with Severely Bounded Communication

We study auctions with severe bounds on the communication allowed: each bidder may only transmit t bits of information to the auctioneer. We consider both welfare- and profit-maximizing auctions under this communication restriction. For both measures, we determine the optimal auction and show that the loss incurred relative to unconstrained auctions is mild. We prove non-surprising properties of these kinds of auctions, e.g., that in optimal mechanisms bidders simply report the interval in which their valuation lies in, as well as some surprising properties, e.g., that asymmetric auctions are better than symmetric ones and that multi-round auctions reduce the communication complexity only by a linear factor

Strategic Payments in Financial Networks

In their seminal work on systemic risk in financial markets, Eisenberg and Noe [Larry Eisenberg and Thomas Noe, 2001] proposed and studied a model with n firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation - if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of ?(n) away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems

Cooperative games with overlapping coalitions

In the usual models of cooperative game theory, the outcome of a coalition formation process is either the grand coalition or a coalition structure that consists of disjoint coalitions. However, in many domains where coalitions are associated with tasks, an agent may be involved in executing more than one task, and thus may distribute his resources among several coalitions. To tackle such scenarios, we introduce a model for cooperative games with overlapping coalitions—or overlapping coalition formation (OCF) games. We then explore the issue of stability in this setting. In particular, we introduce a notion of the core, which generalizes the corresponding notion in the traditional (non-overlapping) scenario. Then, under some quite general conditions, we characterize the elements of the core, and show that any element of the core maximizes the social welfare. We also introduce a concept of balancedness for overlapping coalitional games, and use it to characterize coalition structures that can be extended to elements of the core. Finally, we generalize the notion of convexity to our setting, and show that under some natural assumptions convex games have a non-empty core. Moreover, we introduce two alternative notions of stability in OCF that allow a wider range of deviations, and explore the relationships among the corresponding definitions of the core, as well as the classic (non-overlapping) core and the Aubin core. We illustrate the general properties of the three cores, and also study them from a computational perspective, thus obtaining additional insights into their fundamental structure

Spatial SINR Games of Base Station Placement and Mobile Association

We study the question of determining locations of base stations that may belong to the same or to competing service providers. We take into account the impact of these decisions on the behavior of intelligent mobile terminals who can connect to the base station that offers the best utility. The signal to interference and noise ratio is used as the quantity that determines the association. We first study the SINR association-game: we determine the cells corresponding to each base stations, i.e., the locations at which mobile terminals prefer to connect to a given base station than to others. We make some surprising observations: (i) displacing a base station a little in one direction may result in a displacement of the boundary of the corresponding cell to the opposite direction; (ii) A cell corresponding to a BS may be the union of disconnected sub-cells. We then study the hierarchical equilibrium in the combined BS location and mobile association problem: we determine where to locate the BSs so as to maximize the revenues obtained at the induced SINR mobile association game. We consider the cases of single frequency band and two frequency bands of operation. Finally, we also consider hierarchical equilibria in two frequency systems with successive interference cancellation

Quality of Information, Survival, and Incentives

This dissertation is devoted to questions on long run survival, the optimal elicitation of private information, and the optimal order of gathering information. In Chapter 2, I consider an infinite horizon risk sharing game in which players have heterogeneous priors about future endowments, and analyze asymptotic behavior of efficient allocation depending on whether the players have commitment power and whether the players are Bayesian or ambiguity averse (Gilboa and Schmeidler (1989)). As in Blume and Easley (2006), I show that if the players are expected utility maximizing Bayesian learners and have commitment power, only survivors are those with the least incorrect beliefs. All other players starve in the long run. In other cases, no player vanishes. When the players are Bayesian and have no commitment power, no player starves in a Pareto efficient subgame perfect equilibrium. When the players are ambiguity averse and have commitment power, they can agree on a stationary allocation, which means that no player vanishes. When the players are ambiguity averse and have no commitment power, for sufficiently large discount factors, a stationary Pareto efficient allocation with commitment is a subgame perfect equilibrium. In Chapter 3, I consider a principal-agent problem in which a principal elicits an agent’s information when the quality of information provided by the agent depends on the agent’s type. We investigate the impact of the agent’s type dependent outside option on the optimal contract. Under restrictive assumptions on the type dependent outside option and the agent’s vii information structure, I show that the principal admits bad types and good types, but reject intermediate types. By further restricting our attention to a smaller class of decision problems, I show the existence of an optimal contract and construct how to design an optimal contract. Finally, I provide an example in which the principal optimally hires bad types to reduce the expected payment to good types. In the example, the principal actually loses if the agent draws a bad type. In Chapter 4, co-authored with Professor Tilman B¨orgers, we study the optimal order of experimentation, considering a class of dynamic decision problems in which two experiments are available and a decision maker incurs costs of experimentation. Given the class of two binary experiments, there is no non-trivial comparison of sequential experiments. The reason why the decision maker runs a less informative experiment first in some circumstances is because the less informative experiment triggers the second experiment less frequently than the more informative experiment does. This idea allows us to come up with another class of two experiments, for which there exists non-trivial comparison of experiments. Given the second class of experiment, informativeness of static decision problems implies informativeness of dynamic decision problems. That is, it is optimal for the decision maker to run a more informative experiment first in every decision problem under study.PHDEconomicsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/147638/1/kyhan_1.pd

Essays in information economics and communication

Communication and Public Goods, Bayesian Persuasion with Private Experimentation, Crisis and Credit Rating Agencie

Contractual and Organizational Structurewith Reciprocal Agents

Empirically, compensation systems generate substantial effort despite weak monetary incentives. We consider reciprocal motivations as a source of incentives. We solve for the optimal contract in the basic principal-agent problem and show that reciprocal motivations and explicit performance-based pay are substitutes. A firm endogenously determines the mix of the two sources of incentives to best induce effort from the agent. Analyzing extended versions of the model allows us to examine how organizational structure impacts the effectiveness of reciprocity and to derive specific empirical predictions. We use the UK-WERS workplace compensation data set to confirm the predictions of our extended model.optimal contracts, reciprocity, organizational structure