Yuan Ju

Reconciling marginalism with egalitarianism: consistency, monotonicity, and implementation of egalitarian Shapley values

One of the main issues in economic allocation problems is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide three different characterizations of egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, from the perspective of a variable player set, we show that all these solutions satisfy the same reduced game consistency. Second, on a fixed player set, we characterize this class of solutions using monotonicity properties. Finally, towards a strategic foundation, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game. These characterizations discover fundamental differences as well as intriguing connections between marginalism and egalitarianism.

The Consensus Value for Games in Partition Function Form

This paper studies a procedural and axiomatic extension of the consensus value [cf. Ju et al. (2007)] to the class of partition function form games. This value is characterized as the unique function that satisfies efficiency, complete symmetry, the quasi-null player property and additivity. By means of the transfer property, a second characterization is provided. Moreover, it is shown that the consensus value satisfies individual rationality under a superadditivity condition, and well balances the tradeoff between coalitional effects and externality effects. In this respect, explicit differences with other solution concepts are indicated.

Rational bargaining in games with coalitional externalities

This paper provides a flexible strategic framework to analyze bargaining and values in environments with coalitional externalities. Within this framework we propose a new value that extends the Shapley value to partition function form games, the so-called Rational Belief Shapley (RBS) value. We investigate the strategic foundation of the RBS value by constructing an implementation mechanism. This mechanism extends existing models of multilateral bargaining by allowing players a higher degree of freedom to form coalitions. The same framework of bidding and renegotiation allows for natural variations of the RBS-mechanism. In this way, alternative “Shapley-like” values are obtained, and a unified platform to analyze and compare these solutions is provided.

Auctioning and Selling Positions: A Non-Cooperative Approach to Queuing Conflicts

Complementary to the axiomatic and mechanism design studies on queueing problems, this paper proposes a strategic bargaining approach to resolve queueing conflicts. Given a situation where players with different waiting costs have to form a queue in order to be served, they firstly compete with each other for a specific position in the queue. Then, the winner can decide to take up the position or sell it to the others. In the former case, the rest of the players will proceed to compete for the remaining positions in the same manner; whereas for the latter case the seller can propose a queue with corresponding payments to the others which can be accepted or rejected. In this paper we show that, when the players are competing for the first position in the queue, then the subgame perfect equilibrium outcome of the corresponding mechanism coincides with the well-known maximal transfer rule, while an efficient queue is always formed in equilibrium. We also argue that changing the mechanism so that the players compete for the last position implements the minimal transfer rule. The analysis discovers a striking relationship between pessimism and optimism in this type of decision making.

Efficiency and compromise: a bid-offer–counteroffer mechanism with two players

A bid-offer–counteroffer mechanism is proposed to solve a fundamental two-person decision choice problem with two alternatives. It yields a unique subgame perfect equilibrium outcome, and leads to an intuitive overall solution that offers a reconciliation between egalitarianism and utilitarianism. We then investigate the axiomatic foundation of the solution. Furthermore, we compare it with several conventional strategic approaches to this setting.

Compensating Losses and Sharing Surpluses in Project-Allocation Situations

By introducing the notions of projects and shares, this paper studies a class of economic environments, the so-called project-allocation situations, in which society may profit from cooperation, i.e., by reallocating the initial shares of projects among agents.This paper mainly focuses on the associated issues of compensation of losses and surplus sharing arising from the reallocation of projects.For this purpose, we construct and analyze an associated project-allocation game and a related system of games that explicitly models the underlying cooperative process.Speciffic solution concepts are proposed.

Consistency, Monotonicity and Implementation of Egalitarian Shapley Values

One of the main issues in economics is the trade-off between marginalism and egalitarianism. In the context of cooperative games this trade-off can be framed as one of choosing to allocate according to the Shapley value or the equal division solution. In this paper we provide tools that make it possible to study this trade-off in a consistent way by providing three types of results on egalitarian Shapley values being convex combinations of the Shapley value and the equal division solution. First, we show that all these solutions satisfy the same reduced game consistency. Second, we characterize this class of solutions using monotonicity properties. Finally, we provide a non-cooperative implementation for these solutions which only differ in the probability of breakdown at a certain stage of the game.

A Non-Cooperative Approach to the Compensation Rules for Primeval Games

To model inter-individual externalities and analyze the associated compensation issue, Ju and Borm (2005) introduces a new game-theoretic framework, primeval games, and proposes, from a cooperative perspective, three compensation rules as solution concepts for primeval games: the marginalistic rule, the concession rule, and the primeval rule. In this paper, we provide a non-cooperative approach to address these problems more specifically. Inspired by the generalized bidding approach (Ju and Wettstein (2006)) for TU games, we design various bidding mechanisms to fit the model of primeval games and show that each implements the corresponding compensation rule in subgame perfect equilibrium. These mechanisms require nearly no condition on the game environment and obtain each solution itself rather than in expected terms.Moreover, since the various mechanisms share a common basic structure, this paper offers a non-cooperative benchmark to compare different axiomatic solutions, which, in return, may advance the axiomatic study of the issue by constructing alternative compensation rules.