Discrete Bidding Strategies for a Random Incoming Order

作者：Bressan Alberto^*; Facchi Giancarlo

来源：SIAM Journal on Financial Mathematics, 2014, 5(1): 50-70.

DOI：10.1137/130917685

• measure-valued optimization
• optimality conditions
• optimal pricing strategy
• bidding game
• Nash equilibrium
• limit order book

This paper is concerned with a model of a one-sided limit order book, viewed as a noncooperative game for n players. Agents offer various quantities of an asset at different prices, ranging over a finite set Omega(nu) = {(i/nu) (P) over bar; i = 1,...,nu}, competing to fulfill an incoming order, whose size X is not known a priori. Players can have different payoff functions, reflecting different beliefs about the fundamental value of the asset and probability distribution of the random variable X. For a wide class of random variables, we prove that the optimal pricing strategies for each seller form a compact and convex set. By a fixed point argument, this yields the existence of a Nash equilibrium for the bidding game. As nu -> infinity, we show that the discrete Nash equilibria converge to an equilibrium solution for a bidding game where prices range continuously over the whole interval [0, (P) over bar].

• 出版日期2014