TY - GEN

T1 - Incentives in effort games

AU - Bachrach, Yoram

AU - Rosenschein, Jeffrey S.

PY - 2008

Y1 - 2008

N2 - We consider Effort Games, a game theoretic model of co-operation in open environments, which is a variant of the principal-agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; achieving certain subsets of the tasks completes the project successfully, while others do not. The probability of achieving a task is higher when the agent in charge of it exerts effort, at a certain cost for that agent. A central authority, called the principal, attempts to incentivize agents to exert effort, but can only reward agents based on the success of the entire project. We model this domain as a normal form game, where the payoffs for each strategy profile are defined based on the different probabilities of achieving each task and on the boolean function that defines which task subsets complete the project and which do not. We view this boolean function as a simple coalitional game, and call this game the under-lying coalitional game. We show that finding the minimal reward that induces an agent to exert effort is at least as hard computationally as finding the Banzhaf power index in the underlying coalitional game, so this problem is #P-hard in general. We also show that in a certain restricted domain, where the underlying coalitional game is a unanimity weighted voting game with certain properties, it is possible to solve all of the above problems in polynomial time.

AB - We consider Effort Games, a game theoretic model of co-operation in open environments, which is a variant of the principal-agent problem from economic theory. In our multiagent domain, a common project depends on various tasks; achieving certain subsets of the tasks completes the project successfully, while others do not. The probability of achieving a task is higher when the agent in charge of it exerts effort, at a certain cost for that agent. A central authority, called the principal, attempts to incentivize agents to exert effort, but can only reward agents based on the success of the entire project. We model this domain as a normal form game, where the payoffs for each strategy profile are defined based on the different probabilities of achieving each task and on the boolean function that defines which task subsets complete the project and which do not. We view this boolean function as a simple coalitional game, and call this game the under-lying coalitional game. We show that finding the minimal reward that induces an agent to exert effort is at least as hard computationally as finding the Banzhaf power index in the underlying coalitional game, so this problem is #P-hard in general. We also show that in a certain restricted domain, where the underlying coalitional game is a unanimity weighted voting game with certain properties, it is possible to solve all of the above problems in polynomial time.

UR - http://www.scopus.com/inward/record.url?scp=84899971938&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84899971938

SN - 9781605604701

T3 - Proceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS

SP - 1517

EP - 1520

BT - 7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008

PB - International Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)

T2 - 7th International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS 2008

Y2 - 12 May 2008 through 16 May 2008

ER -