THE SIGNALING GAME OF A FIRM WITH UNKNOWN PROFITABILITY AND AN INVESTOR

Abstract

A relationship between a firm and a potential investor, when a firm is in the need of funds to take advantage of a valuable investment opportunity, is modeled as a signaling game. The goal of the article is to revise a game theory model of R. Gibbons, in which an investor does not know whether the profitability of a firm is high or low, in a moment when he needs to accept or reject an equity stake offered in exchange for the funds needed for the project's realization. The signaling game of a firm and an investor is shown graphicly along with the description of conditions, under which there is the existence of separating or pooling equilibrium. In an extended model, a function is defined for describing the lowest equity stake in a firm, which a rational investor would accept when there are three types of firms in a market. A wider set of possible equilibriums is analyzed by defining the level lines of the function. Conditions under which there is the existence of a separating, a semi-separating, and a pooling equilibrium, are described analytically and graphicly. In this way, a clear insight is gained as to which share of financially attractive projects is not realized due to the problem of incomplete information in the signal game of firms and investors.

Keywords

• game theory
• signaling game
• bayesian theorem
• information asymmetry
• investment