Game-theoretic Solution Concepts Research Articles

NETWORK EXCHANGE AS A COOPERATIVE GAME

This paper presents parallels between network exchange experiments and N-person cooperative games with transferable utility, to show how game theory can assist network exchange researchers, not only in predicting outcomes, but in properly specifying the scope of their models. It illustrates how utility, strategy and c-games, concepts found in game theory, could be used by exchange theorists to help them reflect on their models and improve their research design. One game theoretic solution concept, the kernel, is compared to recent network exchange algorithms as an illustration of how easy it is to apply game theory to the exchange network situation. It also illustrates some advantages of using a game theory solution concept to model network exchange.

Frequency-Dependent Stability for Two-Species Interactions

Evolutionary game theory is extended to models of two-species interactions where fitnesses are based on individual characteristics (strategies) rather than on a population dynamic that assumes homogeneous species. It is shown that the coevolutionary theories in the literature that combine ecology with genetic viability selection are part of this extended theory and that the dynamic stability resulting from a separation of ecological and evolutionary processes actually follows from game-theoretic solution concepts. The main focus of the paper is to investigate the application of the ESS (evolutionarily stable strategy) solution concept to dynamic stability when fitnesses are given by random interactions between individuals as opposed to viability selection. For two-species frequency-dependent interactions, the ESS criterion that implies stability asserts that, in any system near the ESS, at least one of the species is better off (i.e., more fit) if it evolves towards the ESS. The global stability of a polymorphic two-species ESS that is shown for two-species matrix games gives a powerful tool to predict the course of evolution through static fitness comparisons.

A Game Theoretic Approach to Problems in Telecommunication

This paper considers two specific problems in telecommunication, namely the Terrestrial Flight Telephone System and the rerouting of international telephone calls. Both situations are modelled as coalitional games, and game theoretic techniques are used to tackle the problems. It is shown that a special class of coalitional games emerges from the situations under consideration and that the structure of the situations has theoretical implications, including the coincidence of several game theoretic solution concepts. The implications of these theoretical results for the two practical problems are discussed.

A Characterization of Game-Theoretic Solutions which Lead to Impossibility Theorems

For some game-theoretic solution concepts, such as dominant strategies, Nash equilibrium, and undominated strategies, only dictatorial social choice functions are implementable on a full domain of preferences with at least three alternatives. For other solution concepts, such as the iterative removal of weakly dominated strategies, undominated Nash equilibrium, and maximin, it is possible to implement non-dictatorial social choice functions. Which aspects of solution concepts accounts for these differences? We answer this question by providing a characterization of solution concepts which lead to impossibility results.

An efficient characterization of some cost allocation solutions associated with capacitated network design problems

We analyze some game-theoretic solution concepts associated with a cost allocation problem arising from the Capacitated Network Design (CND) problem. The problem is formulated as a cost cooperative game in characteristic function form to be referred to as the CND game. We provide an efficient representation of several game-theoretic solution concepts associated with the CND game. In particular, we efficiently characterize the core, and in some cases the nucleolus, the least weighted?-core and a certain "central" point in the least weighted?-core. Our model properly generalizes several previously studied cooperative games. We also employ our model to analyze cost allocation problems associated with several classes of network design problems, which were not previously studied in the literature. Specifically, we efficiently characterize the above cost allocation solutions for cost allocation problems associated with the Capacitated Concentrator Location problem, the Capacitated Minimum Spanning Tree problem, the Capacitated Fixed Cost Spanning Forest problem, and the Capacitated Steiner Tree problem.

Joint Coherence in Games of Incomplete Information

Decisions are often made under conditions of uncertainty about the actions of supposedly-rational competitors. The modeling of optimal behavior under such conditions is the subject of noncooperative game theory, of which a cornerstone is Harsanyi's formulation of games of incomplete information. In an incomplete-information game, uncertainty may surround the attributes as well as the strategic intentions of opposing players. Harsanyi develops the concept of a Bayesian equilibrium, which is a Nash equilibrium of a game in which the players' reciprocal beliefs about each others' attributes are consistent with a common prior distribution, as though they had been jointly drawn at random from populations with commonly-known proportions of types. The relation of such game-theoretic solution concepts to subjective probability theory and nonstrategic decision analysis has been controversial, as reflected in critiques by Kadane and Larkey and responses from Harsanyi, Shubik, and others, which have appeared in this journal. This paper shows that the Bayesian equilibrium concept and common prior assumption can be reconciled with a subjective view of probability by (i) supposing that players elicit each others' probabilities and utilities through the acceptance of gambles, and (ii) invoking a multi-agent extension of de Finetti's axiom of coherence (no arbitrage opportunities, a.k.a. “Dutch books”). However, the Nash property of statistical independence between players is weakened, and the probability distributions characterizing a solution of the game admit novel interpretations.

Negotiation Analysis: A Characterization and Review

“Negotiation analysis” seeks to develop prescriptive theory and useful advice for negotiators and third parties. It generally emphasizes the parties' underlying interests (as distinct from the issues on the table and the positions taken), alternatives to negotiated agreement, approaches to productively manage the inherent tension between competitive actions to “claim” value individually and cooperative ones to “create” value jointly, as well as efforts to change perceptions of the game itself. Since advice to one side does not necessarily presume the full game-theoretic rationality of the other side(s), negotiation analysts often draw on the findings of behavioral decision analysts and economists. Further, this approach does not generally assume that all the elements of the “game” are common knowledge. Thus, the negotiation analytic approach tends to de-emphasize the application of game-theoretic solution concepts or efforts to find unique equilibrium outcomes. Instead, to evaluate possible strategies and tactics, negotiation analysts generally focus on changes in perceptions of the “zone of possible agreement” and the (subjective) distribution of possible negotiated outcomes conditional on various actions. This approach is especially sensitive to potentially unrealized joint gains. It has been used to develop prescriptive advice for the simplest bilateral negotiations between monolithic parties, for negotiations through agents or with linked “internal” and “external” aspects, for negotiations in hierarchies and networks, as well as for more complex coalitional interactions.

Communication between rational agents

Conventional game-theoretic solution concepts never guarantee meaningful communication in cheap-talk games. I define a solution concept which does guarantee communication in some games. I assume full rationality without imposing equilibrium conditions, but add a natural behavioral assumption about how agents use language: agents have a propensity to speak the truth and to believe others speak the truth, but use the game's strategic incentives to check whether such behavior and beliefs are rational. I also define and prove the existence of an equilibrium version of the concept, and present examples where its predictions seem more natural than Farrell's neologism-proof equilibrium.

Explorations in aggregating choices

A choice is understood as any function which picks a subset from each set of alternatives. Such choices are aggregated here in four different ways: through composition, choice-union and two procedures inspired by game-theoretic solution concepts, namely the non-cooperative and the von Stackelberg. In each case we are interested in the extent to which certain well-known choice-theoretic properties are preserved by the aggregation studied. In closing, we regard certain algebraic aspects of aggregations and means of choices, remarking on their ethical implications.

The P-Set: A Structure-Induced Equilibrium for Sequential Legislative Voting

Legislative voting is a formally defined collective decision-making process that includes a relatively small number of participants. Thus one might expect that process to be effectively modeled by a number of game-theoretic solution concepts and for legislatures to be important laboratories for testing hypotheses derived from game theory. The failure to realize these expectations is understandable if one attempts to interpret the solution concepts in a legislative context: restrictive voter preference requirements and questionable incentives for agenda formation raise serious doubts about the efficacy of existing game theoretic solutions for modeling legislative voting decisions. The P-set is developed from the sequential structure of legislative voting, and the assumption that legislator decisions to add an issue to that sequence are based on the maximin principle. It addresses both questions of agenda and outcome stability. In general, the P-set maximizes existence by relaxing the normally stringent preference conditions for stability. In this paper consideration is given to problems associated with the application of game-theoretic solution concepts to the analysis of legislative voting decisions. In particular these solutions, which qualify as preference-induced equilibria, raise questions about how elements in a solution set come before the voters. To answer these questions, an alternative approach to stability in collective choice is proposed. The P-set is a structure-induced equilibrium, derived from the sequential order of legislative voting that enables legislators to anticipate and respond to the consequences of adding to the sequence of issues that forms a voting decision.'

Vote trading: An experimental study

This essay reports the results of ninety 3-person and 5-person bargaining experiments using several alternative vote trading scenarios. These experiments are designed to test: (1) Riker and Brams' controversial hypothesis that vote trading can yield inferior outcomes as against the alternative hypothesis that vote trading induces ‘market-like’ efficiency in voting bodies; (2) the relative adequacy of several game theoretic solution concepts for vote trading games without a Condorcet winner (core); and, (3) the adequacy of the core itself. First, on the basis of eighteen experiments with binding commitments, we find some support for Riker and Brams' hypothesis: in nine trials, subjects first trade to a Pareto dominated outcome. In five of these trials, however, these outcomes are eventually displaced by Pareto efficient ones. Without binding commitments, however, we find little support for the ‘paradox of vote trading’ hypothesis. Specifically, while six of seven trials of a 3-person game yield ‘equitable’ outcomes, seventeen trials of several 5-person games without binding commitments strongly support the competitive solution as a cooperative game solution concept, and suggest that the V-set and M 1 bargaining set are either redundant or useless. Seven trials each of six 5-person games with a condorcet winner (core), however, suggest that usual static solution concepts may be inadequate for treating games with any interesting degree of strategic complexity.

On the Difficulty of Attaining Distributional Goals with Imperfect Information about Consumers

Abstract Recently, mechanisms which overcome the free rider problem and achieve Pareto optimality under imperfect information have been constructed. In this paper we provide various impossibility theorems which show the difficulty of achieving distributional goals when consumers’ tastes are unknown. The results are developed for a particular game theoretic solution concept, that of dominant strategy; they could be extended if, instead, Bayesian equilibrium were the solution concept. As a way out we propose a second-best approach to welfare optimization.

The Effects of Communication and Information Availability in an Experimental Study of a Three-Person Game

This study investigated the effects of six communication/information conditions on the outcomes reached by three-person groups playing a characteristic function game. The game was played by a monopolist and two weaker players. The conditions consisted of six combinations which varied the amount of information available to the players and their ability to communicate with one another. The investigation focused on the effects of the independent variables and the relationship between the data and several game theoretic solution concepts. The results indicated that the monopolist's payoffs depended to a large extent on the communication/information conditions. Announcement of the payoff division and the availability of messages tended to reduce his payoffs. In conditions where no messages were allowed, the monopolist's payoffs increased over time. Although the data diverged significantly from the core, the situations which contributed to greater competition resulted in outcomes closer to the core. A comparison between von Neumann-Morgenstern solutions and the more general class of subsolutions indicated that subsolutions were more reflective of the behavior observed. In addition, the results over the entire set of conditions closely approximated the Shapley value, which has recently been shown to be a risk neutral player's expected utility for playing the game. Directions for future research were suggested.

The kernel and payoffs in European government coalitions

This paper attempts to analyze the process of coalition formation in the European parliamentary democracies in terms of existing concepts from game theory. The game theory approach rests first of all on the assumption of individual, or actor, optimizing behavior in some particular situation or game. For relatively simple situations various solution concepts can be developed. If some actual parliamentary situation may be modelled by a game like structure, then the various game theoretic solution concepts may be developed to produce solution predictions, and these may be compared with the events that did occur. The match between prediction and observation may however be poor. If this is the case then one may infer that the essential assumption of optimizing behavior could not be justified. This inference is however infertile, since the game theory developments rest on the existence of unobservables, the utility functions or the like, and we can not explore the nature of such unobservables. A second inference may be that the game theory model does not catch the significant features of the parliamentary game. While it is possible to develop game theory models of high generality, such models do not generate simple solution notions. The predictions therefore are too

A Research Note on the Predictive Adequacy of the Kernel

The kernel, a game-theoretic solution concept, was tested competitively against minimum resource and pivotal power theories. Experimental data from six veto and six nonveto weighted-majority games served as the basis of the test. The kernel proved to be consistently inferior to both minimum resource and pivotal power theories in predicting payoffs.

Sequential games of status

In this paper we use classical and behavioral game theory to predict coalition behavior in a sequential three-person laboratory game. In the laboratory situation used for the three studies reported in this paper, each player seeks to maximize the rank of his final accumulated point score in relation to the total scores of the other members of his triad. We assume that, unable to solve the sequential game as a single supergame, each player forms a simplified representation of the situation by adopting short-run, surrogate objectives for the outcome of each game in the sequence. In particular, we assume that each player seeks to maximize the status of his current total score during each game in the sequence. Given these surrogate objectives, we represent each trial in the sequential game as a distinct game of status in characteristic set function form. Using this formal model of the situation, we extend a solution concept from n-person game theory to identify which of the possible outcomes of each game in the sequence are, in a game theoretic sense, stable. We then add the assumption that each player obeys a bargaining maxim prescribing that coalition members should agree to an outcome in which one partner outranks the other if and only if he also enjoys higher rank when the coalition forms. We modify the game theoretic solution by considering only outcomes that conform to the bargaining maxim. The behavioral modification substantially improves the success game theory achieves in predicting rank outcomes observed in the three laboratory studies. However, with or without the modification, the game theoretic solution concept fails to predict which coalitions form in these studies. Finally, we develop an alternative theory that predicts not only the rank outcomes of each game in the sequence but also the probability that each coalition forms. The empirical success enjoyed by this theory in predicting the ranks acquired on each game is greater than that attained by the unmodified game theoretic predictions, and is nearly comparable to that achieved by the behaviorally modified game theoretic solution. Moreover, the alternative theory's robust coalition predictions are strongly supported by the results from the three laboratory studies.

The assignment game I: The core

The assignment game is a model for a two-sided market in which a product that comes in large, indivisible units (e.g., houses, cars, etc.) is exchanged for money, and in which each participant either supplies or demands exactly one unit. The units need not be alike, and the same unit may have different values to different participants. It is shown here that the outcomes in thecore of such a game — i.e., those that cannot be improved upon by any subset of players — are the solutions of a certain linear programming problem dual to the optimal assignment problem, and that these outcomes correspond exactly to the price-lists that competitively balance supply and demand. The geometric structure of the core is then described and interpreted in economic terms, with explicit attention given to the special case (familiar in the classic literature) in which there is no product differentiation — i.e., in which the units are interchangeable. Finally, a critique of the core solution reveals an insensitivity to some of the bargaining possibilities inherent in the situation, and indicates that further analysis would be desirable using other game-theoretic solution concepts.