My research focuses on game theory and mechanism design. I am specializing in multi-person environments with varying coalition structure or changing network connections. I have been working on both axiomatic approaches of cooperative solution concepts and strategic approaches of noncooperative bargaining models. My research also covers various applications including industrial organization, marketing strategies, political economics, and public economics. Here I state my research in three categories, 1) cooperative decision making, 2) noncooperative coalitional bargaining with strategic alliance, and 3) mechanism design in networks.
I am interested in axiomatic characterizations of cooperative solution concepts. My research has focused on the properties of allocation rules with varying population or changing network.
[1] ``Sequentially Two-Leveled Egalitarianism for TU Games: Characterization and Application,''
European Journal of Operational Research (2012, with Theo S.H. Driessen)
The paper introduces a new cooperative one-point solution concept for transferable utility games, namely sequentially two-leveled egalitarian value, which compromises marginalism and egalitarianism. It assigns each player her separable contribution, which is the average of her values of the smaller games, and distributes the remaining parts equally. The value is characterized by efficiency, linearity, symmetry, and so called scale-dummy player property, replacing the dummy player property, which is used in the axiomatization of the Shapley value. In the application to a land-corn production economy, it yields an allocation, in which the landlord's interest coincides with striving for a maximum production level. For economies with the linear production function, not only the landlord but also all the workers have strict incentives to increase the scale of the economy.
[2] ``Sequential Contributions Rules for Minimum Cost Spanning Tree Problems,''
Mathematical Social Sciences (2012, with Youngsub Chun)
This paper concerns how to share the total construction cost among the participated agents in minimum cost spanning tree problems and proposes a family of cost sharing rules. Each rule in the family assigns an agent part of the cost of connecting him to his immediate predecessor, and all of his followers are equally responsible for the remaining part. It is characterized by imposing the axioms of efficiency, non-negativity, independence of following costs, group independence, and weak first-link consistency. The Bird rule (Bird, 1976) and the sequential equal contributions rule - originated from Littlechild and Owen (1973) - are two distinguished members of the family. The Bird rule is obtained by requiring an agent to pay the entire cost of connecting him to his immediate predecessor, and the sequential equal contributions rule is obtained by requiring an agent and each of his followers to be equally responsible for this cost. We also provide additional axioms to single out those rules from the family.
In addition to the published papers, I plan to work on allocation problems in networks such as river sharing problems and pipeline construction problems. Among many ideas, I am currently studying about a so-called decentralized greedy algorithm, which is a network version of simultaneous eating algorithm - initially proposed by Bogomolnaia and Moulin (2001). Applying this decentralized algorithm to minimum cost spanning tree problems, the planner can find a minimum cost spanning tree and allocate the total cost according to the Folk solution by assigning a specific construction responsibility to each agent.
To make up for the lack of strategic foundations of cooperative game theory, I am working on noncooperative bargaining models. My research in this area includes my two job market papers. In the papers, I study a new noncooperative coalitional bargaining model which allows both buyout options and strategic coalition formation. That is, each player can strategically choose bargaining partners and form a coalition by buying out other players' resources and rights with upfront transfers.
Thus, when players form a coalition, they not only consider the surplus from the coalition itself, but also take into account their bargaining power in the subsequent bargaining game. In this model, I investigate inefficiency and gradualism as a result of players' strategic alliance behavior. This model also shows how `freedom of association' can reduce the inequality of the payoff distribution. One can think this project combines Baron and Ferejohn (1989) / Okada (1996) and Gul (1989).
[3] ``Bargaining and Buyout'' (Job Market Paper #1)
The paper deals with general characteristic function form games, in which each subcoalition generates a different worth. The paper investigates the effect of allowing players' strategic alliance on efficiency and equality. First, I provide a general inefficiency result: an efficient stationary subgame perfect equilibrium is generically impossible if the discount factor is sufficiently high but strictly less than 1. That is, a player strategically forms an inefficient coalition as a transitional state to improve her bargaining power. Second, I study how the strategic alliance behavior reduces inequality in two applications: for three-player simple games, the equilibrium payoff vector Lorenz-dominates both the Shapley-Shubik power index and the core-constrained Nash bargaining solution; and for wage bargaining games, workers endogenously form a union and their equilibrium payoffs can be greater than marginal products.
[4] ``Noncooperative Unanimity Games in Networks'' (Job Market Paper #2)
Partial or local cooperation is sometime inevitable at least in a transitional state for informational or physical reasons.
In this paper, I apply the noncooperative bargaining model with buyout options to network-restricted games, in which players can cooperate only with their neighbors. In this paper, to investigate the effect of network with controlling network-irrelevant factors, I focus on unanimity games, in which only a grand-coalition generates a positive surplus.
We characterize a condition on network structures for efficient equilibria. Only in complete or circular networks, an efficient stationary subgame perfect equilibrium exists for all discount factors. In any other network, an efficient stationary subgame perfect equilibrium is impossible for a sufficiently high discount factor. I also provide an example in which social welfare decreases as more communication is possible.
The model is quite flexible to be applied into various environments. Among many interesting applications, I am working on assignments games, in which each link in a bipartite graph generates a surplus. In this environment, players may form a with-in-part coalition, though it produces nothing. This will provide strategic foundations of collusive behaviors in trading networks. On the other hand, for computational tractability in large games, I also plan to apply my model to a continuous-time framework.
For a seller, attracting buyers is an essential part of marketing strategies. Bulow and Klemperer (1996) show that a seller is better off by adding an extra buyer to compete in a standard auction, rather than finding the optimal mechanism in fixed buyers. In many situations, however, the seller can contact only part of buyers directly and attracting new buyers usually requires costs. Then, what would be the best way to increase participants? To answer this question, I model an environment with asymmetric contact information and study mechanisms which make agents refer their neighbors.
[5] ``Incentives on Referrals: VCG Mechanisms and Multi-Level Mechanisms'' (Working Paper)
An environments with asymmetric contact information is considered. In addition to a payoff type, which represents a preference over allocations, each agent has a connection type, which determines his neighbors. The participants and the feasible allocations are endogenously determined by agents' strategic referrals. First, I generalize VCG mechanisms, in which the mechanism designer compensates each agent for his marginal contribution. Alternatively, I introduce multi-level mechanisms, in which each agent is compensated by the agents who would not be able to participate without his referrals. I characterize conditions for these mechanisms to be individually rational, budget surplus, and incentive compatible in both fully referring their neighbors and truthfully telling their preferences.
[6] ``Optimal Auctions with Referrals: Carrots and Sticks'' (Work in Progress)
A referral program is one of the pervasive marketing strategies. For some markets such as hair shops, medical services, contact lenses, housing, and financial markets, referral programs are widely spread; however, for some other markets, sellers rely on traditional marketing tools like a public advertisement. I study optimal auctions with referral programs in a simple selling environment. An item is sold by a seller and there are two buyers; one existing buyer and one potential buyer. The potential buyer can participate in the market only through the existing buyer's referral. The seller is not sure whether the existing buyer can contact the potential buyer. This simple model explains why referral programs are widely spread in specialized markets in which only a few customer has a high valuation.
As future research along this line, I will study dynamic mechanisms. As I found in [6], the effectiveness of a referral program crucially depends on the distribution of buyers' valuations. Hence, if the good is durable or easily resold, referral programs may not work effectively. For a better understanding of this general environment, I plan to allow a secondary market in which an existing buyer can resell the good to the potential buyer.
Bibliography
BARON, D. AND J. FEREJOHN (1989): ``Bargaining in legislatures,'' The American Political Science Review, 1181-1206.
BIRD, C. (1976): ``On cost allocation for a spanning tree: a game theoretic approach,'' Networks, 6, 335-350.
BOGOMOLNAIA, A. AND H. MOULIN (2001): ``A new solution to the random assignment problem,'' Journal of Economic Theory, 100, 295-328.
BULOW, J. AND P. KLEMPERER (1996): ``Auctions Versus Negotiations,'' The American Economic Review, 86, 180-194.
GUL, F. (1989): ``Bargaining foundations of Shapley value,'' Econometrica: Journal of the Econometric Society, 81-95.
LITTLECHILD, S. C. AND G. OWEN (1973): ``A simple expression for the Shapley value in a special case,'' Management Science, 20, 370-372.
OKADA, A. (1996): ``A noncooperative coalitional bargaining game with random proposers,'' Games and Economic Behavior, 16, 97-108.