David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Theory and Decision 45 (3):201-240 (1998)
This paper proposes a revised Theory of Moves (TOM) to analyze matrix games between two players when payoffs are given as ordinals. The games are analyzed when a given player i must make the first move, when there is a finite limit n on the total number of moves, and when the game starts at a given initial state S. Games end when either both players pass in succession or else a total of n moves have been made. Studies are made of the influence of i, n, and S on the outcomes. It is proved that these outcomes ultimately become periodic in n and therefore exhibit long-term predictable behavior. Efficient algorithms are given to calculate these ultimate outcomes by computer. Frequently the ultimate outcomes are independent of i, S, and n when n is sufficiently large; in this situation this common ultimate outcome is proved to be Pareto-optimal. The use of ultimate outcomes gives rise to a concept of stable points, which are analogous to Nash equilibria but consider long-term effects. If the initial state is a stable point, then no player has an incentive to move from that state, under the assumption that any initial move could be followed by a long series of moves and countermoves. The concept may be broadened to that of a stable set. It is proved that every game has a minimal stable set, and any two distinct minimal stable sets are disjoint. Comparisons are made with the results of standard TOM
|Keywords||Game theory Noncooperative games Theory of Moves (TOM) Prisoner's Dilemma Stable set|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Chris Freiling (1984). Banach Games. Journal of Symbolic Logic 49 (2):343-375.
Cristina Bicchieri & Gian Aldo Antonelli (1995). Game-Theoretic Axioms for Local Rationality and Bounded Knowledge. Journal of Logic, Language and Information 4 (2):145-167.
Edward Epsen (2007). Games with Zero-Knowledge Signaling. Studia Logica 86 (3):403 - 414.
Arcady Blinov (1994). Semantic Games with Chance Moves. Synthese 99 (3):311 - 327.
Steven J. Brams (1982). Omniscience and Omnipotence: How They May Help - or Hurt - in a Game. Inquiry 25 (2):217 – 231.
Giacomo Bonanno (2004). Memory and Perfect Recall in Extensive Games. Games and Economic Behavior 47 (2):237-256.
Steven J. Brams & D. Marc Kilgour (1988). National Security Games. Synthese 76 (2):185 - 200.
Julius Sensat (1997). Game Theory and Rational Decision. Erkenntnis 47 (3):379-410.
Gerard van Der Laan & René van Den Brink (2002). A Banzhaf Share Function for Cooperative Games in Coalition Structure. Theory and Decision 53 (1):61-86.
Daniel G. Arce M. (1997). Correlated Strategies as Institutions. Theory and Decision 42 (3):271-285.
Jun Zhang, Trey Hedden & Adrian Chia (2012). Perspective-Taking and Depth of Theory-of-Mind Reasoning in Sequential-Move Games. Cognitive Science 36 (3):560-573.
Jonathan Shalev (2002). Loss Aversion and Bargaining. Theory and Decision 52 (3):201-232.
Marion Scheepers (1994). Meager Nowhere-Dense Games (IV): N-Tactics. Journal of Symbolic Logic 59 (2):603-605.
Andrew M. Colman & Michael Bacharach (1997). Payoff Dominance and the Stackelberg Heuristic. Theory and Decision 43 (1):1-19.
Added to index2010-09-02
Total downloads4 ( #254,577 of 1,101,079 )
Recent downloads (6 months)1 ( #290,337 of 1,101,079 )
How can I increase my downloads?