A PROPORTIONAL REWARDS GAME - COMPETITION AMONG HETEROGENEOUS ACTORS

We analyze a non-cooperative game for pure distribution settings. A gr oup of n actors competes for a single prize. The probability to win th e price can be influenced by making an investment. We assume that the winning probabilities of actors are proportional to their investments. The costs of one unit of investment may vary between actors. A low co st of investment can be interpreted as high productivity in this compe tition. We call an actor active if he makes a positive investment. The game has a unique, inefficient Nash-equilibrium. In equilibrium the a ctive actors are remarkably homogeneous with respect to their costs/be nefits. The stability of the number of active actors under small chang es in the costs of investing, and under the introduction or removal of actors is examined. Under mild conditions, if the number n of actors increases, the number of active actors becomes 2 or the proportion of active actors tends to zero at the rate n-1/2.