Non-transferable Utility Value Research Articles

On the values of Bayesian cooperative games with sidepayments

In this paper, we study the solution concept of value in transferable utility (TU) games with asymmetric information. In our model contingent contracts are required to be incentive compatible, and thus utility might not be not fully transferable. Our approach differs from the standard methodology of TU games with complete information, which summarizes the cooperative possibilities through the characteristic function. Instead, we consider a model in which monetary transfers are modeled as additional sidepayments in a non-transferable utility (NTU) game. Our main result states that [18] generalization of the Shapley NTU value and Salamanca (2020) extension of the Harsanyi NTU value are interim utility equivalent in our model with sidepayments. As a consequence of this result, we obtain a generalization of the Shapley TU value to games with incomplete information. Its formula, however, cannot be described by a simple closed form expression as in the case of complete information.

A generalization of the Harsanyi NTU value to games with incomplete information

In this paper, we introduce a solution concept generalizing the Harsanyi non-transferable utility (NTU) value to cooperative games with incomplete information. The so-defined H-solution is characterized by virtual utility scales that extend the Harsanyi-Shapley fictitious weighted-utility transfer procedure. We construct a three-player cooperative game in which Myerson's [Cooperative games with incomplete information. Int. J. Game Theory, 13, 1984, pp. 69-96] generalization of the Shapley NTU value does not capture some negative externality generated by the adverse selection. However, when we explicitly compute the H-solution in this game, it turns out that it prescribes a more intuitive outcome taking into account the informational externality mentioned above.

A Generalization of the Harsanyi NTU Value to Games with Incomplete Information

In this paper, we introduce a solution concept generalizing the Harsanyi non-transferable utility (NTU) value to cooperative games with incomplete information. The so-defined S-solution is characterized by virtual utility scales that extend the Harsanyi-Shapley fictitious weighted utility transfer procedure. We construct a three-player cooperative game in which Myerson’s [Cooperative games with incomplete information. Int. J. Game Theory, 13, 1984, pp. 69-96] generalization of the Shapley NTU value does not capture some “negative” externality generated by the adverse selection. However, when we explicitly compute the S-solution in this game, it turns out that it prescribes a more intuitive outcome which takes into account the above mentioned informational externality.

Nontransferable utility games with fuzzy coalition restrictions

A value for nontransferable utility (NTU) games with fuzzy coalition restrictions is introduced and characterized. In a similar way as the Shapley value for transferable utility (TU) games has been extended in the literature to study games with restricted cooperation, we extend the Shapley NTU value to deal with NTU games in situations in which there are fuzzy dependency relationships among the players.

Forming coalitions and the Shapley NTU value

A simple protocol for coalition formation is presented. First, an order of the players is randomly chosen. Then, a coalition grows by sequentially incorporating new members in this order. The protocol is studied in the context of non-transferable utility (NTU) games in characteristic function form. If (weighted) utility transfers are feasible when everybody cooperates, then the expected subgame perfect equilibrium payoff allocation anticipated before any implemented game is the Shapley NTU value.

An axiomatization of the consistent non-transferable utility value

The Maschler–Owen consistent value for non-transferable utility games is axiomatized, by means of a marginality axiom.

A Walrasian approach to bargaining games

The paper presents and discusses an alternative approach to bargaining games. N-person bargaining games with complete information are shown to induce in a canonical way an Arrow-Debreu economy with production and private ownership. The unique Walras stable competitive equilibrium of this economy is shown to coincide with an asymmetric Nash bargaining solution of the underlying game with weights corresponding to the shares in production. In the case of an economy with equal shares in production, the unique competitive equilibrium coincides with the symmetric Nash bargaining solution. As this in turn represents the unique Shapley nontransferable utility (NTU) value our paper solves a problem posed by Shubik, namely to find a model in which the Shapley NTU value is a Walrasian equilibrium. “There has been some controversy about the interpretation of the λ-transfer-value … no consensus has yet emerged on the significance of these concerns, which had been addressed… in numerous explorations of the λ-transfer-value as a tool for analysing games and markets … ” (Roth, 1985).

Game theory and applications

Contributed Papers: Refinement of Nash Equilibrium: The Main Ideas. Supergames. Infinitely Repeated Games with Incomplete Information. Repeated Games. Bounded Rationality and Strategic Complexity in Repeated Games. The Shapley Value. Advances in Value Theory. Axiomatizations of the Core, The Nucleolus, And the Prekernel. Consistency Principle. Discrete Concepts in N-Person Game Theory: Nondegeneracy and Homogeneity. Two-Sided Matching Markets: An Overview of Some Theory and Empirical Evidence. Strategic Market Game Models of Exchange Economies. Information Transmission. Monotonic Surplus Sharing and the Utilization of Common Property Resources. Developments in Stable Set Theory. Game Theoretic Models of Voting in Multidimensional Issue Spaces. Israel and the PLO: A Game with Differential Information . A Survey of Some Results Closely Related to the Knaster-Kuratowski-Mazurkiewz Theorem. Selected Abstracts: On the Core of the Assignment Game. The Second Welfare Theorem in Nonconvex Economies. An Evolutionary Game Theory Model for Risk-Taking. Values of Nonatomic Vector Measure Games: Are They Linear Combinations of the Measures? Subgame-Perfect Equilibria in Discrete and Continous Games-Does Discretization Matter? To Vote or Not to Vote: What Is the Quota? Some Bounds for the Banzhaf Index and Other Semivalues. Comparative Cooperative Games Theory. Escalation and Cooperation in International Conflicts-The Dollar-Auction Revisited. An Axiomatization of the Nonsymmetric Nontransferable Utility Value. A Milnor Condition for Nonatomic Lipschitz Games and Its Applications. Zero-Sum Nonstationary Stochastic Games with General State Space. Perfect Equilibrium Points and Lexicographic Domination. A Two-Person Repeated Bargaining Game with Long-Term Contracts. Independence of Irrelevant Alternative and Revealed Group Preferences. The Sealed-Bid Mechanism: An Experimental Study. Rate of Convergence to Full Efficiency in the Buyers' Bid Double Auction as the Market Becomes Large Stationary Strategies in Deterministic Games. Big Boss Games, Clan Games, And Information Market Games. Large Games and Economics with Near-Exhaustion of Gains to Coalition Formation. Values of Large Finite Games. Index.

An axiomatization of the weighted NTU value

Non-symmetric generalizations of the non-transferable utility (NTU) are defined and characterized axiomatically. The first of these is a weighted NTU value that is identical to the (symmetric) NTU value when players have the same weights. On the class of transferable utility games, this weighted NTU value coincides with the weighted Shapley value and on the pure bargaining games it coincides with the non-symmetric Nash bargaining solution. A further extension, the random order NTU value, is also defined and axiomatized and its relationship to the core is discussed.

Power and public goods

A game-theoretic analysis using the Harsanyi-Shapley nontransferable utility value indicates that the choice of public goods in a democracy is not affected by who has voting rights. This is corroborated by an independent economic argument based on the implicit price of a vote.

A theory of the spoils system

In a spoils system, it is axiomatic that ‘to the winners go the spoils.’ This essay formalizes spoils systems as cooperative games, with winners given by a simple game structure, and represented by a fixed number of political appointments. We analyze the resulting spoils games by means of the non-transferable utility value, and we offer two practical applications of the results.

On the Non-Transferable Utility Value: A Reply to Aumann

On the Non-Transferable Utility Value: A Reply to Aumann

Values of Voting Games

The Shapley-Shubik index of political power measures the probability that a given player in a simple game is pivotal, with th2 power to turn a losing coalition into a winning coalition. Until now, this index has been applied only to games with transferable utility. This paper considers the case where utility is not transferable. A voting game is a nontransferable utility game with a simple gane structure. The solution of a voting game is its nontransferable utility value. This paper studies the values of such games. In particular, the Shapley-Shubik index is the value for a certain class of voting games. This shows that the measurement of political power does not depend on the transferability of utility.

An Axiomatization of the Non-Transferable Utility Value

Abstract : The NTU (Non-Transferable Utility) Value is a solution concept for multiperson cooperative games in which utility is not transferable (games without side payments). Introduced by Shapley in (1969), it generalizes his (1953) value for TU (Transferable Utility) games. Many economic contexts are more naturally modelled by NTU than by TU games; and indeed, the NTU value has been applied with some success to a variety of economic and economic-political models. Two well-known applications are Nash's solutions (1950, 1953) for the bargaining problem and for two-person cooperative games, both of which are instances of the NTU value. In this paper, the author offers an axiomatization of the NTU value. Like any axiomatization, it should enable us to understand the concept better, and hence to focus discussion. One can now view the NTU value as defined by the axioms, with the treatment in Shapley (1969) serving as a formula or method of calculation. Thus the NTU value joins the ranks of the TU value and Nash's solution to the bargaining problem, each of which is defined by axioms, but usually calculated by a formula -- a formula whose intuitive significance is not, on the face of it, entirely clear.

On the Non-Transferable Utility Value: A Comment on the Roth-Shafer Examples

On the Non-Transferable Utility Value: A Comment on the Roth-Shafer Examples

Voting for Public Goods

It is shown that when resources are privately owned, the institution of voting is irrelevant to the choice of non-exclusive public goods: the total bundle of such goods produced by Society is the same whether or not minority coalitions are permitted to produce them. This is in sharp contrast to the cases of redistribution and of exclusive public goods, where public decisions depend strongly on the vote. The analytic tool used is the Harsanyi-Shapley non-transferable utility value.

Power and Taxes in a multi-commodity economy

Taxation and redistribution in a democratic majority-rule society are analyzed, using the Harsanyi-Shapley non-transferable utility value. The context is that of a multi-commodity pure exchange economy. Two approaches are treated: one in which taxes are in kind and exchange takes the form of barter; and one in which taxes are in money, exchange takes the form of sale and purchase, and prices are determined by a process of supply and demand. It is shown that in the presence of a non-atomic continuum of agents, the two approaches are equivalent, but that this is not so when there are only finitely many agents. It is also shown that the value exists under both approaches, and a characterization is found in the non-atomic case.