A BAYESIAN GAME FOR A PROFIT AND LOSS SHARING CONTRACT

Abstract

This paper presents a Bayesian Game model for a profit-and-loss sharing (PLS) contract. We develop our model into two parts, namely the model for non-social bank and the model for social bank. We propose the model to reduce adverse selection problem in offering a PLS contract. The Bayesian game starts with an incomplete information. Islamic banks do not know exactly what type of agent is applying for a PLS contract, efficient or non-efficient, the information of the bank is incomplete. In Bayesian game, we assume that the Islamic Bank assigns the agent type with a prior probability. Determination of the profit-sharing ratio of the contract will be discussed. We look for the Bayesian Nash equilibrium of the game in our model which is considered a solution. We show that the bank offers an interesting but risky contract to the agent if the bank assigns that the agent is efficient with a high probability, otherwise the bank offers a less risky contract to the agent if the bank assigns that the agent is a non-efficient agent with high probability. The results can be considered by Islamic banks to reduce the adverse selection problem in PLS contract.