Grim trigger

Abstract: Using the infinitely repeated prisoners' dilemma game as a modeling platform, we examine how domestic political institutions affect the ability of nations to trust and cooperate with each other. We propose a strategy, the agent-specific grim trigger, in which national leaders direct punishments for past defections at the leader of the nation responsible rather than at the nation itself. Leaders refuse to cooperate with those leaders who have cheated them in the past. However, by being prepared to cooperate with new leaders, cooperation can be restored. The focus of punishment on specific agents of the people (leaders), rather than the nation itself, means that citizens want to remove leaders who defect. Hence, domestically accountable leaders pay audience costs for failing to cooperate. These costs make accountable leaders more trustworthy and foster greater cooperation. In contrast, when replacing leaders is difficult, cooperation is less robust; and once cooperation falters, agent-specific punishment policies often lead to prolonged hostilities and periods of acrimonious relations between states.

Abstract: We use a novel experimental design to identify the strategies used by subjects in an infinitely repeated prisoners’ dilemma experiment. We ask subjects to design strategies that will play in their place. We find that the strategy elicitation has negligible effects on behavior supporting the validity of this method. We study the strategies chosen by the subjects and find that they include some commonly mentioned strategies, such as tit-for-tat and Grim trigger. However, other strategies which are thought to have some desirable properties, such as win-stay-lose-shift are not prevalent. The results indicate that what strategy is used to support cooperation changes with the parameters of the game. Finally, our results confirm that long run miss-coordination can arise.

Abstract: In a multihop wireless network, routing a packet from source to destination requires cooperation among nodes. If nodes are selfish, reputation-based mechanisms can be used to sustain cooperation without resorting to a central authority. Within a hop-by-hop reputation-based mechanism, every node listens to its relaying neighbors, and the misbehaving ones are punished by dropping a fraction of their packets, according to a Tit-for-tat strategy. Packet collisions may prevent a node from recognizing a correct transmission, distorting the evaluated reputation. Therefore, even if all the nodes are willing to cooperate, the retaliation triggered by a perceived defection may eventually lead to zero throughput. A classical solution to this problem is to add a tolerance threshold to the pure Tit-for-tat strategy, so that a limited number of defections will not be punished. In this paper, we propose a game-theoretic model to study the impact of collisions on a hop-by-hop reputation-based mechanism for regular networks with uniform random traffic. Our results show that the Nash Equilibrium of a Generous Tit-for-tat strategy is cooperative for any admissible load, if the nodes are sufficiently far-sighted, or equivalently if the value for a packet to the nodes is sufficiently high with respect to the transmission cost. We also study two more severe punishment schemes, namely One-step Trigger and Grim Trigger, that can achieve cooperation under milder conditions.

Abstract: We use a novel experimental design to identify subjects’ strategies in an infinitely repeated prisoners’ dilemma experiment. We ask subjects to design strategies that will play in their place. We find no clear evidence that eliciting strategies affected subjects’ behavior, supporting the validity of this method. We find the chosen strategies include some well-known ones such as Always Defect, Tit-For-Tat and Grim trigger. However, other strategies that are considered to have desirable properties, such as Win-Stay-Lose-Shift, are not prevalent. A majority of subjects use simple strategies that only condition on the previous period’s outcome. We also find that the strategies used to support cooperation change with the parameters of the game. We use the elicited strategies to test our ability to recover strategies using observed cooperate-defect choices and find that we can do so under certain conditions.