Abstract
| Original language | Undefined |
|---|---|
| Pages (from-to) | 107-115 |
| Number of pages | 8 |
| Journal | International game theory review |
| Volume | 7 |
| Issue number | 1 |
| Publication status | Published - 2005 |
Keywords
- METIS-225221
Cite this
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A Note on Repeated Games with Vanishing Actions. / Joosten, Reinoud A.M.G.
In: International game theory review, Vol. 7, No. 1, 2005, p. 107-115.Research output: Contribution to journal › Article › Academic › peer-review
TY - JOUR
T1 - A Note on Repeated Games with Vanishing Actions
AU - Joosten, Reinoud A.M.G.
PY - 2005
Y1 - 2005
N2 - A two-person general-sum repeated game with vanishing actions is an infinitely repeated game where the players face the following restrictions. Each action must be used by player k ¿ {1,2} at least once in every rk ¿ ¿ consecutive stages, otherwise the action vanishes for the remaining play. We assume that the players wish to maximize their limiting average rewards over the entire time-horizon.A strategy-pair is jointly convergent if for each action pair a number exists to which the relative frequency with which this action pair is chosen, converges with probability one. A pair of feasible rewards is called individually rational if each player receives at least the threat-point reward, i.e., the amount which he can guarantee himself regardless of what the opponent does given r1, r2 and the actions available in the long run. In a repeated game with vanishing actions, there may exist multiple threat points which are endogenous to the play.We prove that all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Furthermore, each convex combination of individually-rational jointly-convergent pure-strategy rewards, can be supported by an equilibrium for m × n-games provided r1 > m ¿ 2, r2 > n ¿ 2. Keywords: Stochastic games; vanishing actions; limiting Average rewards; endogenous threats
AB - A two-person general-sum repeated game with vanishing actions is an infinitely repeated game where the players face the following restrictions. Each action must be used by player k ¿ {1,2} at least once in every rk ¿ ¿ consecutive stages, otherwise the action vanishes for the remaining play. We assume that the players wish to maximize their limiting average rewards over the entire time-horizon.A strategy-pair is jointly convergent if for each action pair a number exists to which the relative frequency with which this action pair is chosen, converges with probability one. A pair of feasible rewards is called individually rational if each player receives at least the threat-point reward, i.e., the amount which he can guarantee himself regardless of what the opponent does given r1, r2 and the actions available in the long run. In a repeated game with vanishing actions, there may exist multiple threat points which are endogenous to the play.We prove that all individually-rational jointly-convergent pure-strategy rewards can be supported by an equilibrium. Furthermore, each convex combination of individually-rational jointly-convergent pure-strategy rewards, can be supported by an equilibrium for m × n-games provided r1 > m ¿ 2, r2 > n ¿ 2. Keywords: Stochastic games; vanishing actions; limiting Average rewards; endogenous threats
KW - METIS-225221
M3 - Article
VL - 7
SP - 107
EP - 115
JO - International game theory review
JF - International game theory review
SN - 0219-1989
IS - 1
ER -