# Strategic enforcement of linear payoff relations in a three-player strictly alternating prisoner’s dilemma game

## TL;DR

This paper explores how players can enforce specific outcomes in a three-player prisoner’s dilemma game where turns alternate.

## Contribution

The study introduces Zero-Determinant strategies in a strictly alternating three-player model of the prisoner’s dilemma.

## Key findings

- Zero-Determinant strategies in the alternating model differ from those in simultaneous three-player games.
- Feasible regions for equalizer and extortion strategies are derived in the alternating framework.
- The findings reveal new strategic control mechanisms in multi-player alternating interactions.

## Abstract

The prisoner’s dilemma game is a fundamental model in game theory for studying the emergence of cooperation among self-interested individuals with conflicting incentives. Most existing studies have examined the simultaneous two-player version, where both players act simultaneously. In contrast, this paper investigates the impact of Zero-Determinant strategies in a strictly alternating three-player repeated model of the prisoner’s dilemma game, where players take turns making decisions based on the previous actions of their opponents (one-memory strategy). Analytical results reveal that the Zero-Determinant strategies in the strictly alternating model differ significantly from those in the simultaneous three-player prisoner’s dilemma game. We further examine the equalizer and extortion subsets of Zero-Determinant strategies and derive their feasible regions within this framework. These findings provide new insights into the strategic control and cooperation mechanisms in multi-player alternating interactions.