Shot Game Research Articles

Le "Dilemme des prisonniers": Les arguments d'une coopération en information incomplète

For a "Prisoners' dilemma" played in a cooperative and incomplete information context we look for individually rational, incentive compatible and equilibrated side-payments. We show that the existence and the characteristics of these solution transfers are strongly related to the information conveyed by the payoff vectors of the game itself. For the class of one shot games for which no "cooperative solution" exists and when these games are played a finite or infinite number of times (whatever the discount factor), we show that players can obtain more than the non-cooperative gain in the first period and the maximum collective profit from the second period on.

Internal correlation in repeated games

This paper characterizes the set of all the Nash equilibrium payoffs in two player repeated games where the signal that the players get after each stage is either trivial (does not reveal any information) or standard (the signal is the pair of actions played). It turns out that if the information is not always trivial then the set of all the Nash equilibrium payoffs coincides with the set of the correlated equilibrium payoffs. In particular, any correlated equilibrium payoff of the one shot game is also a Nash equilibrium payoff of the repeated game.For the proof we develop a scheme by which two players can generate any correlation device, using the signaling structure of the game. We present strategies with which the players internally correlate their actions without the need of an exogenous mediator.

THE EFFECTS OF THE EXTRINSIC REWARD AND OF THE LEVEL OF PERFORMANCE ON INTRINSIC MOTIVATION

The main purpose of this study is to investigate the effects of performance-relevant reward on intrinsic motivation by examining both Deci's theory (1975) and Ross's one (1976).Fifty-four female undergraduates were assingned to 6 conditions of 9 Ss each. Reward condition (performance-relevant reward or no reward) was combined factorially with the level of performance (high performance, low performance, or control) in a 2×3 design. The level of performance was manipulated with bogus feedback concerning Ss' ability at the task.Each S performed “a shot game” in one of the 6 conditions, and then evaluated the task interest and enjoyment. Following this phase, Ss were given 8 minutes of free choice time during which observations were made on the amount of time they spent working on the task.The principal findings were as follows;(a) In the control condition, reward left intrinsic motivation unchanged.(b) In both high and low performance condition, reward decreased intrinsic motivation.(c) In no reward condition, intrinsic motiyation in both high and low performance condition enhanced compared with that in the control condition.(d) The above effects were seen only in persistency Ss spent working on the task during free choice time, but no effects of reward occurred on the task evaluation.(e) It was found that the above effects could not be attributed to the fatigue or satiation during the experimental performance phase.Based on the above results, a figural model about the effects of the extrinsic reward and the level of performance upon intrinsic motivation (Fig. 1) was presented, where it was asserted that “the stability of the level of performance” as well as “the level of performance” should be taken account of as an important variable. For example, in “the stable low performance conditions” intrinsic motivation decreases, whereas in “the unstable low performance condtition” it enhances.

A note on the value of zero-sum sequential repeated games with incomplete information

We consider repeated two-person zero-sum games with lack of information on both sides. If the one shot game is played sequentially, it is proved that the sequencevn is monotonic,vn being the value of then shot game. Moreover the speed of convergence is bounded byK/n, and this is the best bound.