Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-10T16:49:36.363Z Has data issue: false hasContentIssue false
  • English
  • Français

Repeated matrix games

Published online by Cambridge University Press:  14 July 2016

Dana B. Kamerud
Dana B. Kamerud*
Affiliation:
St. Louis University
Get access Rights & Permissions [Opens in a new window]

Abstract

A matrix game is played repeatedly, with the actions taken at each stage determining both a reward paid to Player I and the probability of continuing to the next stage. An infinite history of play determines a sequence (Rn) of such rewards, to which we assign the payoff lim supn (R1 + · ·· + Rn). Using the concept of playable strategies, we slightly generalize the definition of the value of a game. Then we find sufficient conditions for the existence of a value and for the existence of stationary optimal strategies (Theorems 8 and 9). An example shows that the game need not have a value (Example 4).

Keywords

STOCHASTIC GAMEREPEATED GAMERECURSIVE GAMENONDISCOUNTED PAYOFFSTATIONARY STRATEGIESPLAYABLE STRATEGIESOPTIMAL STOPPINGTWO-PERSON ZERO-SUM GAMES
Type
Research Papers
Information
Journal of Applied Probability , Volume 16 , Issue 4 , December 1979 , pp. 830 - 842
Copyright
Copyright © Applied Probability Trust 1979 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Breiman, L. (1968) Probability. Addison–Wesley, Reading, MA.Google Scholar
Chung, K. L. (1968) A Course in Probability Theory. Harcourt, Brace and World, New York.Google Scholar
Everett, H. (1957) Recursive games. Ann. Math. Studies 39, 47–78.Google Scholar
Kohlberg, E. (1974) Repeated games with absorbing states. Ann. Statist. 2, 724–738.Google Scholar
Maitra, A. and Parthasarathy, T. (1971) On stochastic games II. J. Optimization Theory Appl. 8, 154–160.Google Scholar
Meyer, P. A. (1966) Probability and Potentials. Blaisdell, Waltham, MA.Google Scholar
Orkin, M. (1972) Recursive matrix games. J Appl. Prob. 9, 813–820.Google Scholar
Parthasarathy, T. (1973) Discounted, positive, and noncooperative stochastic games. Internat. J. Game Theory 2, 25–37.Google Scholar
Shapely, L. S. (1953) Stochastic games. Proc. Natn. Acad. Sci. USA 39, 1095–1100.Google Scholar