Ruijgrok, Matthijs (2012): A singleitem continuous double auction game.

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Abstract
A double auction game with an infinite number of buyers and sellers is introduced. All sellers posses one unit of a good, all buyers desire to buy one unit. Each seller and each buyer has a private valuation of the good. The distribution of the valuations define supply and demand functions. One unit of the good is auctioned. At successive, discrete time instances, a player is randomly selected to make a bid (buyer) or an ask (seller). When the maximum of the bids becomes larger than the minimum of the asks, a transaction occurs and the auction is closed. The players have to choose the value of their bid or ask before the auction starts and use this value when they are selected. Assuming that the supply and demand functions are known, expected profits as functions of the strategies are derived, as well as expected transaction prices. It is shown that for linear supply and demand functions, there exists at most one Bayesian Nash equilibrium. Competitive behaviour is not an equilibrium of the game. For linear supply and demand functions, the sum of the expected profit of the sellers and the buyers is the same for the Bayesian Nash equilibrium and the market where players behave competitively. Connections are made with the ZIC traders model and the $k$double auction.
Item Type:  MPRA Paper 

Original Title:  A singleitem continuous double auction game 
Language:  English 
Keywords:  Continuous double auction; supply and demand; Bayesian Nash equilibrium; ZIC model; kdouble auction 
Subjects:  D  Microeconomics > D4  Market Structure and Pricing > D44  Auctions C  Mathematical and Quantitative Methods > C7  Game Theory and Bargaining Theory > C72  Noncooperative Games 
Item ID:  42086 
Depositing User:  Matthijs Ruijgrok 
Date Deposited:  20. Oct 2012 08:13 
Last Modified:  26. Feb 2013 14:53 
References:  Anufriev M., Arifovic J., Ledyard J., Panchenko V., Efficiency of continuous double auctions under individual evolutionary learning with full or limited information, 2012, Journal of Evolutionary Economics, forthcoming. Chatterjee, K., Samuelson, W., 1983, Bargaining under incomplete information, Operations Research, Vol 31, no. 5, pp 835851. Cliff, D., Bruten, J., 1997, Minimal Intelligence Agents for Bargaining Behaviours in MarketBased Environments. Technical report, HPL9791, Hewlett Packard Labs. Davis D.D., Holt C.A., 1992, Experimental Economics, Princeton University Press, Princeton. Halmos, P., 1950, Measure Theory, Springer Verlag, Berlin. Fano, S., LiCalzi M., Pellizzari P., 2012, Convergence of outcomes and evolution of strategic behavior in double auctions, Journal of Evolutionary Economics, forthcoming. Gode, D.K., Sunder, S., 1993, Allocative Efficiency of Markets with ZeroIntelligence Traders: Market as a Partial Substitute for Individual Rationality, Journal of Political Economy, Vol 101, no. 1, pp. 119137. Jahnsson, 2011. Agentbased modelling as an approach to evaluate the price discovery process in double auction markets, masterthesis Aalto University school of Economics, http://hsepubl.lib.hse.fi/FI/ethesis/pdf/12513/hse_ethesis_12513.pdf} Othman,A., 2008. ZeroIntelligence agents in prediction markets. In: Padgham, L., Parkes, D.C., M\"uller, J., and Parsons, S., eds. Proc. of 7th Int. Conf. on Autonomous Agents and Multiagent Systems (AAMAS 2008). Parsons, S., Marcinkiewicz, M., Niu, J., Phelps, S. Everything you wanted to know about double auctions but were afraid to (bid or) ask. Working Paper, Department of Computer Science, Graduate School and University Center, City University of New York, in preparation. Reny, P.J., Perry, M., 2006, Toward a Strategic Foundation for Rational Expectations Equilibrium, Econometrica, Vol. 74, nr. 5, pp. 12311269. Satterthwaite, M.A., Williams, S.R., 1989, Bilateral trade with the sealed bid kdouble auction: Existence and efficiency, Journal of Economic Theory, Vol 48, nr. 1, pp 107133. Smith V.L., 1962, An experimental study of competitive market behavior, Journal of Political Economy, vol. 70, pp 111137. 
URI:  http://mpra.ub.unimuenchen.de/id/eprint/42086 