In this paper we apply the complete analysis of a normal-form game to a specific non-linear game, deriving from the von Neumann extension of real economic asymetric interaction. The complete analysis of a normal-form game (introduced in literature by D. Carfì) consists of the following examination points: 1c) to find the possible Pareto solutions and crosses; 1d) to find devotion correspondences and devotion equilibria; 1e) to specify the efficiency and noncooperative reachability of devotion equilibria; 2a) to find best reply correspondences and Nash equilibria; 2b) to study the existence of Nash equilibria (Brouwer and Kakutany's fixed point theorems); 2c) to evaluate Nash equilibria: non-cooperative reachability; position with respect to the Pareto boundary and efficiency; 2d) to find dominant strategies, if any; 2e) to find strict and dominant equilibria, to reduce the game by elimination of dominated strategies; 3a) to find conservative values and worst loss functions of the players; 3b) to find conservative strategies and crosses; 3c) to find all the conservative parts of the game (in the bistrategy and biloss spaces); 3d) to find core of the game and conservative knots; 3e) to evaluate Nash equilibria by means of the core and the conservative bi-value; 4a) to find the worst offensive correspondences and the offensive equilibria; 4b) to specify non-cooperative reachability of the offensive equilibria and their efficiency; 4c) to find the worst offensive strategies of each player and the corresponding losses; 4d) to find the possible dominant offensive strategies; 4e) to compare the possible non-cooperative solutions; 5a) to find the elementary best compromises (Kalai-Smorodinsky solutions) and the corresponding biloss; 5b) to find the elementary core best compromise and the corresponding biloss; 5c) to find the Nash bargaining solutions and corresponding bilosses; 5d) to find the solutions with closest bilosses to the shadow minimum; 5e) to find the maximum collective utility solutions; 5f) to confront the possible cooperative solutions.

Study of a game with concave utility space

CARFI', David;
2012

Abstract

In this paper we apply the complete analysis of a normal-form game to a specific non-linear game, deriving from the von Neumann extension of real economic asymetric interaction. The complete analysis of a normal-form game (introduced in literature by D. Carfì) consists of the following examination points: 1c) to find the possible Pareto solutions and crosses; 1d) to find devotion correspondences and devotion equilibria; 1e) to specify the efficiency and noncooperative reachability of devotion equilibria; 2a) to find best reply correspondences and Nash equilibria; 2b) to study the existence of Nash equilibria (Brouwer and Kakutany's fixed point theorems); 2c) to evaluate Nash equilibria: non-cooperative reachability; position with respect to the Pareto boundary and efficiency; 2d) to find dominant strategies, if any; 2e) to find strict and dominant equilibria, to reduce the game by elimination of dominated strategies; 3a) to find conservative values and worst loss functions of the players; 3b) to find conservative strategies and crosses; 3c) to find all the conservative parts of the game (in the bistrategy and biloss spaces); 3d) to find core of the game and conservative knots; 3e) to evaluate Nash equilibria by means of the core and the conservative bi-value; 4a) to find the worst offensive correspondences and the offensive equilibria; 4b) to specify non-cooperative reachability of the offensive equilibria and their efficiency; 4c) to find the worst offensive strategies of each player and the corresponding losses; 4d) to find the possible dominant offensive strategies; 4e) to compare the possible non-cooperative solutions; 5a) to find the elementary best compromises (Kalai-Smorodinsky solutions) and the corresponding biloss; 5b) to find the elementary core best compromise and the corresponding biloss; 5c) to find the Nash bargaining solutions and corresponding bilosses; 5d) to find the solutions with closest bilosses to the shadow minimum; 5e) to find the maximum collective utility solutions; 5f) to confront the possible cooperative solutions.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11570/2325497
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