Daily repetition: A neglected factor in the analysis of electricity auctions

Electricity Journal

Volumn 12, Issue 3, 1999, Pages 60-70

  Rothkopf, Michael H ^a,b  

^a RUTGERS UNIVERSITY   (United States)

^b the State University of New Jersey   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033114707     PISSN: 10406190     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1040-6190(99)00010-X     Document Type: Article

References (21)

1. In this game, each of the two players has two alternative strategies: Cooperate and Defect. The pairs of numbers in the array give the payoffs to Players I and II, respectively, if the players select the corresponding pair of strategies. For example, if Player I chooses Cooperate and Player II chooses Defect, the upper-right- hand pair of numbers indicates that Player I gets a payoff of 0 and Player II gets a payoff of 4.
2. For example, consider a situation in which a product would cost either of two bidders $14 to produce. Suppose that standard sealed bids are being solicited by a buyer for one such item who will only accept bids in $2 increments and who will not pay more than $20 to buy the item. Suppose further that for some odd reason, a bid of $16 is not allowed. A bid of $20 corresponds to the Cooperate strategy, while a Defect strategy corresponds to a bid of $18. No other permitted bid makes sense. If the bidders submit tied bids, a coin flip will select the winner. If each bidder defects, each has an equal chance of winning and an expected profit of $2 (half of $18-$14). If both cooperate, they again each have half a chance of winning, and each has an expected profit of $3. However, if one defects and the other cooperates, the defector wins for sure and gets a profit of $4 while the cooperator gets nothing. In this game, the dominant strategy equilibrium is noncollusive competitive behavior. An auction model that gives rise to a different prisoner's dilemma game arises when two bidders bid for two items, bids are unit prices that must be multiples of $2, the minimum bid is $2, each item is known to be worth $5 to each bidder, and the rules specify that in the event of a tie one bidder gets each item, but that if the bids differ, the high bidder gets to buy one item at her price and one item at the other bidder's price. If both bidders cooperate by bidding $2, each earns $3. If they both bid $4, each earns $1. However, if one bids $4 and the other bids $2, the maker of the higher bid earns $4 while the other bidder gets nothing. Hence, the dominant strategy equilibrium is for both bidders to bid $4.
3. See R. Selten and R. Stoeker, Economic behavior in sequences of finite prisoner's dilemma supergames: A learning theory approach, 7 J. of Econ. Behavior and Organization, 47-70 (1986).
4. The "tit-for-tat" strategy is to start with cooperation and then play on the next play whatever the other player played on the previous one. A "trigger" strategy is to cooperate until your competitor defects, and then always defect.
5. K.O. Kortanek, J.V. Soden and D. Sodaro, Profit analysis and sequential bid pricing models, 20 Mgmt. Sci. 396-417 (1973).
6. S.S. Oren and M.H. Rothkopf, Optimal bidding in sequential auctions, 23 Oper. Res. 1080-1090 (1975).
7. M.H. Rothkopf, A model of rational competitive bidding, 15 Mgmt. Sci. 362-373 (1969).
8. L. Friedman, A competitive bidding strategy, 4 Oper. Res. 104-112 (1956).
9. Rothkopf, Ibid.
10. D.B. Hausch, Multi-object auctions: Sequential vs. Simultaneous sales, 32 Mgmt. Sci. 1599-1610 (1986).
11. A. Ortega-Reichart, Models of Competitive Bidding under Uncertainty, Technical Report No. 8, Department of Operations Research, Stanford University, 1968.
12. M.H. Rothkopf, E. Dougherty and M. Rose, Comment on "multi-object auctions: Sequential vs. Simultaneous sales", 32 Mgmt. Sci. 1611-1612 (1986).
13. J.H. Kagel, Auctions: A Survey of of Experimental Research, April 1992, Dept. of Economics, Univ. of Pittsburgh.
14. R.M. Isaac and J.M. Walker, Information and conspiracy in sealed bid auctions, 6 J. of Econ. Behav. & Org. 139-159 (1985).
15. C.W. Smith, Auctions: The Social Construction of Value, University of California Press (1990).
16. R.M. Harstad, M.H. Rothkopf and K. Waehrer, Efficiency in auctions when bidders have private information about competitors, in M.R. Baye, ed., Advances in Applied Microeconomics, Vol. 6, JAI Press, Greenwich, Connecticut, 1996, at 1-13.
17. P. Milgrom and R. Weber, A theory of auctions and competitive bidding, 50 Econometrica 1089-1122 (1982).
18. R.M. Harstad and M.H. Rothkopf, An 'Alternating Recognition' Model of English Auctions, Rutcor Research Report 34-94, Rutcor, Rutgers Univ. (1994).
19. M.S. Robinson, Collusion and the choice of auction, 16 Rand J. of Econ. 141-145 (1985). See also D.A. Graham and R.C. Marshall, Collusive bidder behavior at single object second price and English auctions, 95 J. of Pol. Econ. 1217-1237 (1987).
20. See, for example, S.S. Oren, A.J. Svoboda and R.B. Johnson, Equity and Efficiency of Unit Commitment in Competitive Electricity Markets, Power Working Paper PWP-039, University of California at Berkeley, June 1996, and R.B. Johnson, A. Svoboda, C. Greif, F. Zhuang, and A. Vojdani, Positioning for a Competitive Electric Industry with PG&E's Hydro-thermal Optimization Model, PG&E paper presented at the Edelman Prize Competition, Informs national meeting, San Diego, May 1997.
21. See, for example, S.S. Oren, A.J. Svoboda and R.B. Johnson, Equity and Efficiency of Unit Commitment in Competitive Electricity Markets, Power Working Paper PWP-039, University of California at Berkeley, June 1996, and R.B. Johnson, A. Svoboda, C. Greif, F. Zhuang, and A. Vojdani, Positioning for a Competitive Electric Industry with PG&E's Hydro-thermal Optimization Model, PG&E paper presented at the Edelman Prize Competition, Informs national meeting, San Diego, May 1997.