Two-person Cooperative Game Research Articles

Conflict Measures in Cooperative Exchange Models of Collective Decision-making

This study focuses on externalities of exchanges of voting positions in collective decision-making. Exchanges are represented by non-constant two-person cooperative games. It is assumed that the rate of exchange is specified by the Raiffa-Kalai-Smorodinsky solution, and a model is specified to identify the exchanges. Externality effects of these exchanges are assessed with two conflict measures we develop here. The measures assess within-group and between-group conflict, respectively, and are applied to collective decision-making in the European Union regarding support for fishery infrastructure. The application shows that the measures provide indispensable insights into the decision-making setting and that these can be used for strategic intervention in the setting. It also shows that both actors' power and the outcomes in exchange with externalities are very different from those in exchange without externalities as studied by theories of network exchange.

Ownership Structure, Value of the Firm, and the Bargaining Power of the Manager

In their seminal article, Michael Jensen and William Meckling developed a theory of corporate ownership structure that took into account the trade-offs available to entrepreneur-manager between inside and outside equity and debt [5, 312]. Jensen and Meckling concentrated on principal-agent problem and agency costs that arise from introduction of outside equity into firm. This was done without any consideration of what effects such an action might have had on bargaining power of owner-manager in negotiating wages with current of firm. Several years later Masahiko Aoki [1; 2, 61-91] introduced a model of firm that emphasized its aspect as a quasi-permanent organization of stockholders and employees [1, 600]. He asserted that as a result of their association with firm, acquire skills and knowledge that, when combined with physical assets supplied by stockholders, can produce some economic gains-the so-called organizational rent. Such rents would not be possible through employment of external factors of production (such as workers that have no knowledge of workings of firm). The organizational rent can be produced only through cooperation of stockholders (supplying physical assets) and existing employees. As such, situation is tantamount to a two-person cooperative game, and question becomes, how then is organizational rent to be distributed between stockholders and employees. Aoki proposed that solution to this particular distribution problem could be accomplished by use of a bargaining process attributed to Frederik Zeuthen and John Harsanyi that leads to Nash bargaining solution. Implicit in Aoki's analysis was that all equity was outside equity. Therefore, no attention was given to how alternative ownership structures of firm affect (1) bargaining power of manager and (2) distribution of organizational rent. One could start out with an ownermanaged firm and examine distribution of organizational rent under such an ownership structure. It would then be important to understand how introduction of outside equity into firm a lt Jensen and Meckling, would affect, if at all, distribution of organizational rent.

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.

The Optimal Management of Transboundary Renewable Resources

This paper investigates the question of the optimal management of renewable resources jointly owned by two states. A dynamic model of fisheries is combined with Nash's theory of two-person co-operative games. Conflicts in the management strategies of the two states arising from differences in perceptions of the social rate of discount, fishing effort costs, and consumer preferences are examined. Cases are considered in which the two partners can and cannot make side or transfer payments to one another. It is concluded that side payments greatly ease the resolution of resource management conflicts. La gestion optimale de ressour-ces renouvelables trans-nationales. Ce memoire examine le problmy renewable resources / 357 should be extended to cover transboundary resources involving several countries. That however, would be the subject of another paper.

Game-theoretic analyses of coalition behavior

Coalitions are frequently more visible than payoffs. The theory of n-person games seeks primarily to identify stable allocations of valued resources; consequently, it gives inadequate attention to predicting which coalitions form. This paper explores a way of correcting this deficiency of game-theoretic reasoning by extending the theory of two-person cooperative games to predict both coalitions and payoffs in a three-person ‘game of status’ in which each player seeks to maximize the rank of his total score. Martin Shubik, ‘Games of Status’, (1971), 117–129. To accomplish this, we analyze the negotiations within each potential two-person coalition from the perspective of Nash's procedure for arbitrating two-person bargaining games, R. Duncan Luce and Howard Raiffa, , John Wiley and Sons, New York, 1958, pp. 121–143. then assume that players expect to achieve the arbitrated outcome selected by this procedure and use these expectations to predict achieved ranks and to identify players' preferences between alternative coalition partners in order to predict the probability that each coalition forms. This work is supported by Research Grant SOC72-05245, awarded to the second author by the National Science Foundation. An earlier version of this paper was presented at the annual meetings of the American Political Science Association, Chicago, Ill., August 29 – September 2, 1974. We thank Peter C. Ordeshook for suggesting that Nash's arbitration model might be applied to this game, and David Deutsch for assisting us in this research. We test these payoff and coalition predictions with data from three laboratory studies, and compare the results with those attained in the same data by von Neumann and Morgenstern's solution of two-person cooperative games, Luce and Raiffa, , pp. 115–119. Aumann and Maschler's bargaining set solution for cooperative n-person games, R. J. Aumann and Michael Maschler, ‘The Bargaining Set for Cooperative Games’, in M. Dresher, L. S. Shapley, and A. W. Tucker (eds.), , Annals Math. Studies, No. 52, Princeton University Press, Princeton, New Jersey, 1964, pp. 443–476. and an alternative model of coalition behavior in three-person sequential games of status. For an extension and application of the bargaining set to three-person games of status and a comparison of the bargaining set with our alternative model of coalition behavior in the three laboratory studies reported in this paper, see Richard J. Morrison's Ph.D. thesis, ‘Rational Choice Models of Coalition Formation in the Triad’, Graduate School of Industrial Administration, Carnegie-Mellon University, Pittsburgh, Pennsylvania, 1974 (this dissertation is available from University Microfilms, Ann Arbor, Michigan); and the paper by Laing and Morrison, ‘Sequential Games of Status’, (1974), 177–197. The coalition model is developed more extensively by Laning and Morrison in “Coalitions and Payoffs in Three-Person Sequential Games: Initial Tests of Two Formal Models”, (1973), 3–26 (hereinafter cited as ‘Initial Tests of Two Formal Models’).

Experiments with cooperative 2 � 2 games

Nash's solution of a two-person cooperative game prescribes a coordinated mixed strategy solution involving Pareto-optimal outcomes of the game. Testing this normative solution experimentally presents problems in as much as rather detailed explanations must be given to the subjects of the meaning of ‘threat strategy’, ‘strategy mixture’, ‘expected payoff’, etc. To the extent that it is desired to test the solution using ‘naive’ subjects, the problem arises of imparting to them a minimal level of understanding about the issue involved in the game without actually suggesting the solution. Experiments were performed to test the properties of the solution of a cooperative two-person game as these are embodied in three of Nash's four axioms: Symmetry, Pareto-optimality, and Invariance with respect to positive linear transformations. Of these, the last was definitely discorroborated, suggesting that interpersonal comparison of utilities plays an important part in the negotiations. Some evidence was also found for a conjecture generated by previous experiments, namely that an externally imposed threat (penalty for non-cooperation) tends to bring the players ‘closer together’ than the threats generated by the subjects themselves in the process of negotiation.

A cooperative game coding scheme

The transmission of a message over a Gaussian channel using a noisy feedback and signals with no bandwidth constraint can be treated as a two-person cooperative game with one of the players stationary. The resultant coding strategy allows error-free transmission at a rate R < R c , the critical signalling rate. An expression for the probability of error is developed for finite values of the transmission interval T. In the case of noiseless feedback, this coding scheme emerges as a generalization of the scheme of Schalkwijk and Kailath.

An example of interaction between information and control: The Transparency of a game

This paper presents an example of a two-person cooperative game, where the control of the first player is at the same time information to the second player. It is proved that, under mild assumptions, the information constraint is transparent, i.e., the players behave as if both had been given the same information by means of a coding system. The consequences of this result are examined for noncooperative games. Finally similar results are obtained for multistep games.

Games with Incomplete Information Played by “Bayesian” Players Part II. Bayesian Equilibrium Points

Part I of this paper has described a new theory for the analysis of games with incomplete information. It has been shown that, if the various players' subjective probability distributions satisfy a certain mutual-consistency requirement, then any given game with incomplete information will be equivalent to a certain game with complete information, called the “Bayes-equivalent” of the original game, or briefly a “Bayesian game.” Part II of the paper will now show that any Nash equilibrium point of this Bayesian game yields a “Bayesian equilibrium point” for the original game and conversely. This result will then be illustrated by numerical examples, representing two-person zero-sum games with incomplete information. We shall also show how our theory enables us to analyze the problem of exploiting the opponent's erroneous beliefs. However, apart from its indubitable usefulness in locating Bayesian equilibrium points, we shall show it on a numerical example (the Bayes-equivalent of a two-person cooperative game) that the normal form of a Bayesian game is in many cases a highly unsatisfactory representation of the game situation and has to be replaced by other representations (e.g., by the semi-normal form). We shall argue that this rather unexpected result is due to the fact that Bayesian games must be interpreted as games with “delayed commitment” whereas the normal-form representation always envisages a game with “immediate commitment.”

Reciprocal reinsurance treaties seen as a two-person co-operative game

Abstract 1.1. In 1930 Professor Cramer wrote: “The object of the theory of risk is to give a mathematical analysis of the random fluctuations in an insurance business, and to discuss the various means of protection against their inconvenient effects” ([6], page 7). This definition has obviously been adequate, since Cramer still subscribes to it when 25 years later he makes a comprehensive survey of the subject [7]. However, the mild complaint Cramer made in 1930 that “practical insurance business has hitherto made little or no application of the results offered by the mathematical theory of risk” still has some validity. The very impressive results achieved by the mathematical theory of risk during the last thirty years have certainly found practical applications, but not so many as one would expect, considering that the theory proposes to analyse the very foundations of the insurance business.

Two-Person Cooperative Games

In this paper, the autor extends his previous treatment of «The Bargaining Problem» to a wider class of situations in which threats can play a role/ A new approach is introduced involving the elaboration of the threat concept.

The Bargaining Problem

A new treatment is presented of a classical economic problem, one which occurs in many forms, as bargaining, bilateral monopoly, etc. It may also be regarded as a nonzero-sum two-person game. In this treatment a few general assumptions are made concerning the behavior of a single individual and of a group of two individuals in certain economic environments. From these, the solution (in the sense of this paper) of classical problem may be obtained. In the terms of game theory, values are found for the game. См. также: Two-person cooperative games, автор - Джо Нэш.