Yoshio Kamijo

A Two-Step Shapley Value for Cooperative Games with Coalition Structures

In this paper, we study cooperative games with coalition structures. We show that a solution concept that applies the Shapley value to games among and within coalitions and in which the pure surplus that the coalition obtains is allocated among the intra-coalition members in an egalitarian way, is axiomatized by modified axioms on null players and symmetric players and the usual three axioms: efficiency, additivity and coalitional symmetry. In addition to the original definition, we give two expressions of this solution concept. One is an average of modified marginal contributions and the other is the weighted Shapley value of a game with restricted communication.

Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value

This study provides a unified axiomatic characterization method of one-point solutions for cooperative games with transferable utilities. Any one-point solution that satisfies efficiency, the balanced cycle contributions property (BCC), and the axioms related to invariance under a player deletion is characterized as a corollary of our general result. BCC is a weaker requirement than the well-known balanced contributions property. Any one-point solution that is both symmetric and linear satisfies BCC. The invariance axioms necessitate that the deletion of a specific player from games does not affect the other players’ payoffs, and this deletion is different with respect to solutions. As corollaries of the above characterization result, we are able to characterize the well-known one-point solutions, the Shapley, egalitarian, and solidarity values, in a unified manner. We also studied characterizations of an inefficient one-point solution, the Banzhaf value that is a well-known alternative to the Shapley value.

Axiomatization of the Shapley value using the balanced cycle contributions property

This paper presents an axiomatization of the Shapley value. The balanced cycle contributions property is the key axiom in this paper. It requires that, for any order of all the players, the sum of the claims from each player against his predecessor is balanced with the sum of the claims from each player against his successor. This property is satisfied not only by the Shapley value but also by some other values for TU games. Hence, it is a less restrictive requirement than the balanced contributions property introduced by Myerson (International Journal of Game Theory 9, 169–182, 1980).

Theoretical and experimental investigations of the performance of keyword auction mechanisms

Two keyword auction mechanisms, the Generalized Second-Price auction (GSP) and the Vickrey-Clarke-Groves mechanism (VCG), were compared theoretically and experimentally. The former is widely used in practice; the latter is not, but it has a dominant strategy equilibrium where all participants bid their true values. In the theoretical investigation, by applying the �locally envy-free Nash equilibrium� to the VCG, we found that the allocations are efficient and that upper and lower bounds of the auctioneers revenue coincide in the two mechanisms. A laboratory experiment, in which the revenues and efficiencies were similar in both mechanisms, supported this result

Sustaining cooperation in social dilemmas: Comparison of centralized punishment institutions

This study investigates two centralized punishment institutions for a linear public goods game. These institutions require a certain contribution level and sanction under-contributing players. The two differ in who, among those who do not meet this requirement, receive sanctions. In one institution, all violators are sanctioned, and in the other, only the worst violator(s) is sanctioned. Theoretically, the public goods game of the latter institution yields contributions equal to or greater than that of the former institution with the same requirement and sanction level. The results of an experiment support this theoretical prediction. However, there is a discrepancy between the theory and laboratory observations in that the institution with the theoretically optimal requirement did not yield the highest profit.

Farsighted Coalitional Stability of a Price Leadership Cartel

This paper analyzes the farsighted behaviour of firms that form a dominant price leadership cartel. We consider stability concepts such as the farsighted core, the farsighted stable sets, and the largest consistent set. We show that: (i) the farsighted core is either an empty set or a singleton set of the grand cartel; (ii) any Pareto efficient cartel is itself a farsighted stable set; and (iii) the set of cartels in which fringe firms enjoy higher profits than the firms in the minimal Pareto efficient cartel is the largest consistent set.

Bidding behaviors for a keyword auction in a sealed-bid environment

A keyword auction is conducted by Internet search engines to sell advertising slots listed on the search results page. Although much of the literature assumes the dynamic bidding strategy that utilizes the current bids of other advertisers, such information is, in practice, not available for participants in the auction. This paper explores the bidding behavior of advertisers in a sealed-bid environment, where each bidder does not know the current bids of others. This study considers secure bidding with a trial bid (SBT) as the bid adjustment process used by the advertisers, which is functional in a sealed-bid environment. It is shown that the SBT bid adjustment process converges to some equilibrium point in a one-shot game irrespective of the initial bid profile. Simulation results verify that a sealed-bid environment would be beneficial to search engines. Bidding behaviors in a sealed-bid keyword auction is analyzed.Even in a sealed bid environment, bidding behavior with a minimal search for others bids leads to a unique fixedpoint.A computer simulation shows that a sealed bid environment is beneficial to a search engine.

Implementation of weighted values in hierarchical and horizontal cooperation structures

This paper studies a non-cooperative mechanism implementing a cooperative solution for a situation in which members of a society are subdivided into groups and/or coalitions and there is asymmetry among the individuals of the society. To describe hierarchical and horizontal cooperation structure simultaneously, we present unified classes of games, the games with social structure, and define a weighted value for these games. We show that our mechanism works in any zero-monotonic environment and implements the Shapley value, the weighted Shapley value, the Owens coalitional value, and the weighted coalitional value, in some special cases.

A new basis and the Shapley value

The purpose of this paper is to introduce a new basis of the set of all TU games. Shapley (1953) introduced the unanimity game in which cooperation of all players in a given coalition yields payoff. We introduce the commander game in which only one player in a given coalition yields payoff. The set of the commander games forms a basis and has two properties. First, when we express a game by a linear combination of the basis, the coefficients related to singletons coincide with the Shapley value. Second, the basis induces the null space of the Shapley value.

A linear proportional effort allocation rule

This paper proposes a new class of allocation rules in network games. Like the solution theory in cooperative games of how the Harsanyi dividend of each coalition is distributed among a set of players, this new class of allocation rules focuses on the distribution of the dividend of each network. The dividend of each network is allocated in proportion to some measure of each players effort, which is called an effort function. With linearity of the allocation rules, an allocation rule is specified by the effort functions. These types of allocation rules are called linear proportional effort allocation rules. Two famous allocation rules, the Myerson value and the position value, belong to this class of allocation rules. In this study, we provide a unifying approach to define the two aforementioned values. Moreover, we provide an axiomatic analysis of this class of allocation rules, and axiomatize the Myerson value, the position value, and their non-symmetric generalizations in terms of effort functions. We propose a new allocation rule in network games that also belongs to this class of allocation rules.