Team reasoning and a measure of mutual advantage in games

The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interacting players in games may sometimes reason as members of a team – a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to satisfy, but a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximum mutual advantage in the games they play

Relative Benefit Equilibrating Bargaining Solution and the Ordinal Interpretation of Gauthier's Arbitration Scheme

In 1986 David Gauthier proposed an arbitration scheme for two player cardinal bargaining games based on interpersonal comparisons of players’ relative concessions. In Gauthier’s original arbitration scheme, players’ relative concessions are defined in terms of Raiffa-normalized cardinal utility gains, and so it cannot be directly applied to ordinal bargaining problems. In this paper I propose a relative benefit equilibrating bargaining solution (RBEBS) for two and n-player ordinal and quasiconvex ordinal bargaining problems with finite sets of feasible basic agreements based on the measure of players’ ordinal relative individual advantage gains. I provide an axiomatic characterization of this bargaining solution and discuss the conceptual relationship between RBEBS and ordinal egalitarian bargaining solution (OEBS) proposed by Conley and Wilkie (2012). I show the relationship between the measurement procedure for ordinal relative individual advantage gains and the measurement procedure for players’ ordinal relative concessions, and argue that the proposed arbitration scheme for ordinal games can be interpreted as an ordinal version of Gauthier’s arbitration scheme

Relative Benefit Equilibrating Bargaining Solution and the Ordinal Interpretation of Gauthier's Arbitration Scheme

In 1986 David Gauthier proposed an arbitration scheme for two player cardinal bargaining games based on interpersonal comparisons of players’ relative concessions. In Gauthier’s original arbitration scheme, players’ relative concessions are defined in terms of Raiffa-normalized cardinal utility gains, and so it cannot be directly applied to ordinal bargaining problems. In this paper I propose a relative benefit equilibrating bargaining solution (RBEBS) for two and n-player ordinal and quasiconvex ordinal bargaining problems with finite sets of feasible basic agreements based on the measure of players’ ordinal relative individual advantage gains. I provide an axiomatic characterization of this bargaining solution and discuss the conceptual relationship between RBEBS and ordinal egalitarian bargaining solution (OEBS) proposed by Conley and Wilkie (2012). I show the relationship between the measurement procedure for ordinal relative individual advantage gains and the measurement procedure for players’ ordinal relative concessions, and argue that the proposed arbitration scheme for ordinal games can be interpreted as an ordinal version of Gauthier’s arbitration scheme

Team Reasoning and a Measure of Mutual Advantage in Games

The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interact- ing players in games may sometimes reason as members of a team—a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to satisfy, but a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximal mutual advantage in the games they play

Team Reasoning and a Measure of Mutual Advantage in Games

The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interact- ing players in games may sometimes reason as members of a team—a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to satisfy, but a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximal mutual advantage in the games they play

Strategic interdependence, hypothetical bargaining, and mutual advantage in non-cooperative games

One of the conceptual limitations of the orthodox game theory is its inability to offer definitive theoretical predictions concerning the outcomes of noncooperative games with multiple rationalizable outcomes. This prompted the emergence of goal-directed theories of reasoning – the team reasoning theory and the theory of hypothetical bargaining. Both theories suggest that people resolve non-cooperative games by using a reasoning algorithm which allows them to identify mutually advantageous solutions of non-cooperative games. The primary aim of this thesis is to enrich the current debate on goaldirected reasoning theories by studying the extent to which the principles of the bargaining theory can be used to formally characterize the concept of mutual advantage in a way which is compatible with some of the conceptually compelling principles of orthodox game theory, such as individual rationality, incentive compatibility, and non-comparability of decision-makers’ personal payoffs. I discuss two formal characterizations of the concept of mutual advantage derived from the aforementioned goal-directed reasoning theories: A measure of mutual advantage developed in collaboration with Jurgis Karpus, which is broadly in line with the notion of mutual advantage suggested by Sugden (2011, 2015), and the benefit-equilibrating bargaining solution function, which is broadly in line with the principles underlying Conley and Wilkie’s (2012) solution for Pareto optimal point selection problems with finite choice sets. I discuss the formal properties of each solution, as well as its theoretical predictions in a number of games. I also explore each solution concept’s compatibility with orthodox game theory. I also discuss the limitations of the aforementioned goal-directed reasoning theories. I argue that each theory offers a compelling explanation of how a certain type of decision-maker identifies the mutually advantageous solutions of non-cooperative games, but neither of them offers a definitive answer to the question of how people coordinate their actions in non-cooperative social interactions

Hypothetical Bargaining and Equilibrium Refinement in Non-Cooperative Games

Virtual bargaining theory suggests that social agents aim to resolve non-cooperative games by identifying the strategy profile(s) which they would agree to play if they could openly bargain. The theory thus offers an explanation of how social agents resolve games with multiple Nash equilibria. One of the main questions pertaining to this theory is how the principles of the bargaining theory could be applied in the analysis of hypothetical bargaining in non-cooperative games. I propose a bargaining model based on the benefit-equilibrating bargaining solution (BES) concept for non-cooperative games, broadly in line with the principles underlying Conley and Wilkie's (2012) ordinal egalitarian solution for Pareto optimal point selection problems with finite choice sets. I provide formal characterizations of the ordinal and the cardinal versions of BES, discuss their application to n-player games, and compare model's theoretical predictions with the data available from several experiments involving `pie games'

Hypothetical Bargaining and the Equilibrium Selection Problem in Non-Cooperative Games

Orthodox game theory is often criticized for its inability to single out intuitively compelling Nash equilibria in non-cooperative games. The theory of virtual bargaining, developed by Misyak and Chater (2014) suggests that players resolve non-cooperative games by making their strategy choices on the basis of what they would agree to play if they could openly bargain. The proposed formal model of bargaining, however, has limited applicability in non-cooperative games due to its reliance on the existence of a unique non-agreement point – a condition that is not satisfied by games with multiple Nash equilibria. In this paper, I propose a model of ordinal hypothetical bargaining, called the Benefit-Equilibration Reasoning, which does not rely on the existence of a unique reference point, and offers a solution to the equilibrium selection problem in a broad class of non-cooperative games. I provide a formal characterization of the solution, and discuss the theoretical predictions of the suggested model in several experimentally relevant games

Team Reasoning and a Measure of Mutual Advantage in Games

The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interact- ing players in games may sometimes reason as members of a team—a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to satisfy, but a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximal mutual advantage in the games they play

Team Reasoning and a Measure of Mutual Advantage in Games

The game theoretic notion of best-response reasoning is sometimes criticized when its application produces multiple solutions of games, some of which seem less compelling than others. The recent development of the theory of team reasoning addresses this by suggesting that interact- ing players in games may sometimes reason as members of a team—a group of individuals who act together in the attainment of some common goal. A number of properties have been suggested for team-reasoning decision-makers’ goals to satisfy, but a few formal representations have been discussed. In this paper we suggest a possible representation of these goals based on the notion of mutual advantage. We propose a method for measuring extents of individual and mutual advantage to the interacting decision-makers, and define team interests as the attainment of outcomes associated with maximal mutual advantage in the games they play