Jointly Controlled Lotteries with Biased Coins

TL;DR

This paper introduces a mechanism using two biased coins to generate any desired distribution securely, even under adversarial conditions, and applies it to prove equilibrium existence in certain quitting games.

Contribution

It presents a novel method for controlled lotteries with biased coins that maintains distribution integrity despite adversarial influence, and applies this to game theory equilibrium proofs.

Findings

Mechanism ensures distribution invariance under adversarial coin outcomes.

Every quitting game with two players having at least two continue actions has an ε-equilibrium.

The approach extends the understanding of secure randomized mechanisms in game theory.

Abstract

We provide a mechanism that uses two biased coins and implements any distribution on a finite set of elements, in such a way that even if the outcomes of one of the coins is determined by an adversary, the final distribution remains unchanged. We apply this result to show that every quitting game in which at least two players have at least two continue actions has an undiscounted $\ep$-equilibrium, for every $\ep > 0$.