K-Implementation

TL;DR

This paper introduces the concept of k-implementation, analyzing the minimal monetary transfers needed to ensure rational agents in a game achieve desired outcomes without altering game rules.

Contribution

It defines and studies k-implementation in complete and incomplete information games, including VCG and mixed strategies, extending mechanism design to more realistic CS scenarios.

Findings

K-implementation quantifies minimal payments for outcome enforcement.

Analysis includes complete and incomplete information settings.

Extends to mixed strategies with correlation devices.

Abstract

This paper discusses an interested party who wishes to influence the behavior of agents in a game (multi-agent interaction), which is not under his control. The interested party cannot design a new game, cannot enforce agents' behavior, cannot enforce payments by the agents, and cannot prohibit strategies available to the agents. However, he can influence the outcome of the game by committing to non-negative monetary transfers for the different strategy profiles that may be selected by the agents. The interested party assumes that agents are rational in the commonly agreed sense that they do not use dominated strategies. Hence, a certain subset of outcomes is implemented in a given game if by adding non-negative payments, rational players will necessarily produce an outcome in this subset. Obviously, by making sufficiently big payments one can implement any desirable outcome. The question is what is the cost of implementation? In this paper we introduce the notion of k-implementation of a desired set of strategy profiles, where k stands for the amount of payment that need to be actually made in order to implement desirable outcomes. A major point in k-implementation is that monetary offers need not necessarily materialize when following desired behaviors. We define and study k-implementation in the contexts of games with complete and incomplete information. In the latter case we mainly focus on the VCG games. Our setting is later extended to deal with mixed strategies using correlation devices. Together, the paper introduces and studies the implementation of desirable outcomes by a reliable party who cannot modify game rules (i.e. provide protocols), complementing previous work in mechanism design, while making it more applicable to many realistic CS settings.