A reformulated Shapley-like value for cooperative games with interval payoffs

In this paper, a new value for cooperative interval games is proposed which may remedy the disadvantages of the interval Shapley-like value and of the improved interval Shapley-like value introduced by Han et al. (2012). Moreover, it is shown that the reformulated interval value uniquely satisfies the properties of efficiency, indifference null player, symmetry, and additivity.     

Persistent equilibria in strategic games

A perfect equilibrium [Selten] can be viewed as a Nash equilibrium with certain properties of local stability. Simple examples show that a stronger notion of local stability is needed to eliminate unreasonable Nash equilibria. The persistent equilibrium is such a notion. Properties of this solution are studied. In particular, it is shown that in each strategic game there exists a pesistent equilibrium which is perfect and proper.     

Genetic learning in strategic form games

We analyze the learning behavior of a Simple Genetic Algorithm in symmetric 3 × 3 Strategic-Form-Games. In cases of contests within one population and also between two populations the behavior of the SGA is compared with the behavior of the replicator dynamics and is analyzed with respect to equilibrium concepts in evolutionary game theory. Furthermore conservative non-adaptive strings are added to the population which lead to convergence to an equilibrium even in “GA-deceptive” games where the equilibrium can not be reached by GAs using only selection and crossover.     

Transfers,contracts and strategic games

This paper analyses the role of transfer payments and strategic contracting within two-person strategic form games with monetary payoffs. First, it introduces the notion of transfer equilibrium as a strategy combination for which individual stability can be supported by allowing the possibility of transfers of the induced payoffs. Clearly, Nash equilibria are transfer equilibria, but under common regularity conditions the reverse is also true. This result typically does not hold for finite games without the possibility of randomisation, and transfer equilibria for this particular class are studied in some detail.     

Improvement dynamics in games with strategic complementarities

In a finite game with strategic complementarities, every strategy profile is connected to a Nash equilibrium with a finite individual improvement path. If, additionally, the strategies are scalar, then every strategy profile is connected to a Nash equilibrium with a finite individual best response improvement path.The first author acknowledges financial support from the Russian Foundation for Basic Research (grant 02-01-00854) and from a presidential grant for the state support of the leading scientific schools (NSh-1843.2003.01); he also thanks Universidad Carlos III de Madrid, Departamento de Economía, and personally Francisco Marhuenda for their hospitality. The other authors would like to thank Michihiro Kandori, Akihiko Matsui, Jim Friedman, Claudio Mezzetti, and Federico Echenique for helpful comments. All the three thank an anonymous referee and the Editor of this journal for bringing us together and suggesting the merger of two independent works.     

On consistent solutions for strategic games

Nash equilibria for strategic games were characterized by Peleg and Tijs (1996) as those solutions satisfying the properties of consistency, converse consistency and one-person rationality.  There are other solutions, like the ɛ-Nash equilibria, which enjoy nice properties and appear to be interesting substitutes for Nash equilibria when their existence cannot be guaranteed. They can be characterized using an appropriate substitute of one-person rationality. More generally, we introduce the class of “personalized” Nash equilibria and we prove that it contains all of the solutions characterized by consistency and converse consistency. Received January 1996/Final version December 1996     

Onn-person noncooperative multicriteria games described in strategic form

This paper undertakes the problem of multicriteria decision support in conflict situations described as a noncooperative game. Construction of such a decision support requires the development of the noncooperative game theory to be generalized for the multicriteria case. New theoretical results in this case are presented. Features of the multicriteria noncooperative games are shown with use of a duopoly model in case of two goods and two criteria of each player. Concepts of the decision support are discussed.     

The consistency principle for games in strategic form

We start with giving an axiomatic characterization of the Nash equilibrium (NE) correspondence in terms of consistency, converse consistency, and one-person rationality. Then axiomatizations are given of the strong NE correspondence, the coalition-proof NE correspondence and the semi-strong NE. In all these characterizations consistency and suitable variants of converse consistency play a role. Finally, the dominant NE correspondence is characterized. We also indicate how to generalize our results to Bayesian and extensive games.     

Values for strategic games in which players cooperate

In this paper we propose a new method to associate a coalitional game with each strategic game. The method is based on the lower value of finite two-player zero-sum games. We axiomatically characterize this new method, as well as the method that was described in Von Neumann and Morgenstern (1944). As an intermediate step, we provide axiomatic characterizations of the value and the lower value of matrix games and finite two-player zero-sum games, respectively.The authors acknowledge the financial support of Ministerio de Ciencia y Tecnologia, FEDER andXunta de Galicia through projects BEC2002-04102-C02-02 and PGIDIT03PXIC20701PN.We wish to thank Professor William Thomson as well as an anonymous referee for useful comments.     

Existence of minmax points in discontinuous strategic games

In this note we prove the existence of minmax points for strategic form games where the sets of strategies are topological spaces and the payoff functions satisfy conditions weaker than continuity. The employed tools are the class of transfer weakly upper continuous functions and the class of weakly lower pseudocontinuous functions. An example shows that our result is of minimal character.     

Real options in strategic investment games between two asymmetric firms

This paper examines strategic investment games between two firms that compete for optimal entry in a project that generates uncertain revenue flows. Under asymmetry on both the sunk cost of investment and revenue flows of the two competing firms, we investigate the value of real investment options and strategic interaction of investment decisions. Compared to earlier models that only allow for asymmetry on sunk cost, our model demonstrates a richer set of strategic interactions of entry decisions. We provide a complete characterization of pre-emptive, dominant and simultaneous equilibriums by analyzing the relative value of leader’s and follower’s optimal investment thresholds. In a duopoly market with negative externalities, a firm may reduce loss of real options value by selecting appropriate pre-emptive entry. When one firm has a dominant advantage over its competitor, both the dominant firm and dominated firm enter at their respective leader’s and follower’s optimal thresholds. When the pre-emptive thresholds of both firms happen to coincide, the two firms enter simultaneously. Under positive externalities, firms do not compete to lead.     

A note on isomorphism and strategic equivalence of cooperative games

In this note, we will give several examples to illustrate that two essential games which are isomorphic are not necessarily S-equivalent when the cores of both games are “small” or empty. In other words, we show that whether two isomorphic games are S-equivalent can not be justified in terms of the “size” of the core.     

Single-payoff farsighted stable sets in strategic games with dominant punishment strategies

We investigate farsighted stable sets in a class of strategic games with dominant punishment strategies. In this class of games, each player has a strategy that uniformly minimizes the other players’ payoffs for any given strategies chosen by these other players. We particularly investigate a special class of farsighted stable sets, each of which consists of strategy profiles yielding a single payoff vector. We call such a farsighted stable set as a single-payoff farsighted stable set. We propose a concept called an inclusive set that completely characterizes single-payoff farsighted stable sets in strategic games with dominant punishment strategies. We also show that the set of payoff vectors yielded by single-payoff farsighted stable sets is closely related to the strict \(\alpha \)-core in a strategic game. Furthermore, we apply the results to strategic games where each player has two strategies and strategic games associated with some market models.     

An axiomatic approach to egalitarianism in TU-games

A core concept is a solution concept on the class of balanced games that exclusively selects core allocations. We show that every continuous core concept that satisfies both the equal treatment property and a new property called independence of irrelevant core allocations (IIC) necessarily selects egalitarian allocations. IIC requires that, if the core concept selects a certain core allocation for a given game, and this allocation is still a core allocation for a new game with a core that is contained in the core of the first game, then the core concept also chooses this allocation as the solution to the new game. When we replace the continuity requirement by a weak version of additivity we obtain an axiomatization of the egalitarian solution concept that assigns to each balanced game the core allocation minimizing the Euclidean distance to the equal share allocation.     

Computing the cores of strategic games with punishment–dominance relations

In this paper, we discuss the computational complexity of the strategic cores of a class of n-person games defined by Masuzawa (Int J Game Theory 32:479–483, 2003), which includes economic situations with monotone externality. We propose an algorithm for finding an α-core strategy of any game in this class which, counting the evaluation of a payoff for a strategy profile as one step, terminates after O(n ³· M) operations, where M is the maximum size of a strategy set of any of the n players. The idea underlying this method is based on the property of reduced games. This paper is based on a part of the doctoral dissertation of the author. The author thanks Mikio Nakayama, Masashi Umezawa, William Thomson, an associate editor, and the anonymous referee for their helpful comments, suggestions, and advice. Thanks are also due to Yukihiko Funaki for a comment that led the author to this subject. The author is responsible for errors and inadvertencies.     

A fixed point characterization of the dominance-solvability of lattice games with strategic substitutes

We demonstrate that a lattice game with strategic substitutes is dominance-solvable if and only if there exists a unique fixed point of the function that results from an iteration of the best response function. This finding complements a result of Milgrom and Roberts’ (Econometrica 58:1255–1277, 1990) by which a lattice game with strategic complements is dominance-solvable if and only if there exists a unique Nash equilibrium. We illustrate our main result by an application to a model of Cournot outcome-competition.      

Axiomatizations of team logics

In a modular approach, we lift Hilbert-style proof systems for propositional, modal and first-order logic to generalized systems for their respective team-based extensions. We obtain sound and complete axiomatizations for the dependence-free fragment FO(～) of Väänänen's first-order team logic TL, for propositional team logic PTL, quantified propositional team logic QPTL, modal team logic MTL, and for the corresponding logics of dependence, independence, inclusion and exclusion.As a crucial step in the completeness proof, we show that the above logics admit, in a particular sense, a semantics-preserving elimination of modalities and quantifiers from formulas.     

Computing power indices: Multilinear extensions and new characterizations

Johnston [Johnston, R.J., 1978. On the measurement of power: some reactions to Laver. Environment and Planning A 10, 907–914], Deegan and Packel [Deegan, J., Packel, E.W., 1979. A new index of power for simple n-person games. International Journal of Game Theory 7, 113–123], and Holler [Holler, M.J., 1982. Forming coalitions and measuring voting power. Political Studies 30, 262–271] proposed three power indices for simple games: Johnston index, Deegan–Packel index, and the Public Good Index. In this paper, methods to compute these indices by means of the multilinear extension of the game are presented. Furthermore, a new characterization of the Public Good Index is given. Our methods are applied to two real-world examples taken from the political field.