Case Study: The Strategic Form of Electricity Markets Suppose that we are transported onto the trading floor of PPL Energy Plus (E+) in Allentown Pennsylvania. The power traders are preparing to submit their daily bids to the PJM Independent System Operator (PJM) for the next day’s dispatch. You are one of the traders and your objective is to make lots of money! Here are the rules to participating in the market… All generators must submit a bid by noon of the previous day. A bid includes quantity in terms of megawatts (MW) and price in terms of dollars per megawatt hour (MWH)… A generator can submit multiple bids.
For example: – Generator X is capable of producing 500 MW. It can submit a bid of $5/MWH for 100 MW and a bid of $100/MWH for the remaining 400 MW… Bids are capped at $1, 000 per MWH; this is equivalent to $1 per kilowatt hour (kwh)… PJM post bid results at 4 PM of the previous day… PJM selects the generators with the lowest bids necessary to supply the forecasted next day demand for electricity; all generators chosen for dispatch are paid the same price regardless of their bid, this price referred to as the “clearing price” is the highest bid of the generators selected for dispatch. For example: – Generator A submits a bid of $5/MWH – Generator B submits a bid of $50/MWH – Generator C submits a bid of $500/MWH – Generator D submits a bid of $501/MWH – Generator E submits a bid of $750/MWH – Generator F submits a bid of $999/MWH – Only Generators A, B and C are selected for dispatch, therefore the clearing price is $500/MWH.
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Note, Generators A and B are paid $500/MWH even though their bids were less. Let us now translate this market into a strategic form game: . Players: E+ and Exelon’s PowerTeam. Strategies: An easy way to think of a player’s strategy is the minimum amount the player is willing to accept. In this game, each player will be limited to three strategies: (1) high bid, (2) medium bid, and (3) low bid. The high bid will be $100/MW, which yields a profit of $80/MW.
The medium bid will be $50, which yields a profit of $30. The low bid will be $20, which yields no profit. In addition, it is known that each player has enough capacity to supply 90% of the next day’s demand for electricity, and if both players bid the same price, then they will be dispatched equally… Outcomes: The players who submit less than or equal to the clearing price are the winners since their bids are accepted… Payoffs: The players’ payoffs (profits) are shown in the table below, where D is equal to the next day’s demand for electricity. PowerTeam High Med Low E+ High 0.
5 D 80 = 40 D 0. 5 D 80 = 40 D 0. 1 D 80 = 8 D 0. 9 D 80 = 72 D 0. 1 D 80 = 8 D 0.
9 D 80 = 72 D Med 0. 9 D 80 = 72 D 0. 1 D 80 = 8 D 0. 5 D 30 = 15 D 0. 5 D 30 = 15 D 0. 1 D 30 = 3 D 0.
9 D 30 = 27 D Low 0. 9 D 80 = 72 D 0. 1 D 80 = 8 D 0. 9 D 30 = 27 D 0. 1 D 30 = 3 D 00 Questions: 1) Are there dominant strategies in the game? 2) What bidding strategy do you recommend to E+? 3) What is the nature of competition between E+ and PowerTeam (classify it as strategic complements or strategic substitutes)? Should E+ expand its capacity so that it can serve 100% of the next day’s demand for electricity? 4) What strategy could E+ use to create cooperation? Solutions to Questions: 1) Are there dominant strategies in the game? In examining the payoff table, we find that: . If PowerTeam bids high, then E+’s optimal strategy is to bid medium or low…
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If PowerTeam bids medium, then E+’s optimal strategy is to bid low… If PowerTeam bids low, then E+’s optimal strategy is to bid high… If E+ bids high, then PowerTeam’s optimal strategy is to bid medium or low… If E+ bids medium, then PowerTeam’s optimal strategy is to bid low… If E+ bids low, then PowerTeam’s optimal strategy is to bid high. Hence, neither player has a dominant strategy.
In general, each player’s optimal strategy is to bid one lower than the other player, if the other player bids high or medium, and to bid high, if the other player bids low. 2) What bidding strategy do you recommend to E+? The best strategy for E+ is not clear-cut: . An individual high bid does not generate the highest payout for either E+ or PowerTeam. In fact, the highest payout for a player, $72 times Demand (D), only occurs if the opponent bids high and the player does not… A low bid, on either player’s part, introduces the possibility of generating either the highest profit or no profit…
An individual medium bid ensures a profit and allows for the possibility of being awarded the highest payout… The cooperative game solution would be (High, High).
This solution does not maximize the payout for either player, although it does provide a good payout for both. Additionally, it can also provide a higher payout than the minimum payout on a medium bid. Taking these points into account, and without information as to how PowerTeam might bid, E+ should adopt the strategy of a medium bid. Although this solution does allow for the minimum payout of $3 times Demand, it does provide the possibility of the highest payout.
Therefore, this solution eliminates the possibility of no profit and still allows a chance for maximum payout. 3) What is the nature of competition between E+ and PowerTeam (classify it as strategic complements or strategic substitutes)? Should E+ expand its capacity so that it can serve 100% of the next day’s demand for electricity? The nature of the competition between E+ and PowerTeam is that of strategic substitutes. In other words, they are competing on price, and it will be to one company’s advantage to maintain or lower its bid price, if another company raises theirs. The table below shows the payoffs should E+ implement a 10% increase in bid prices. As seen below, the reaction of PowerTeam to maintain its existing bid prices results in increased profits for PowerTeam, and decreased profits for E+.
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Thus, increasing its bid prices harms E+. PowerTeam High (bid = $100; profit = $80) Med (bid = $50; profit = $30) Low (bid = $20; profit = $0) E+ High (bid = $110; profit = $90) 0. 1 D 90 = 9 D 0. 9 D 90 = 81 D 0. 1 D 90 = 9 D 0.
9 D 90 = 81 D 0. 1 D 90 = 9 D 0. 9 D 90 = 81 D Med (bid = $55; profit = $35) 0. 9 D 80 = 72 D 0. 1 D 80 = 8 D 0. 1 D 35 = 3.
5 D 0. 9 D 35 = 31. 5 D 0. 1 D 35 = 3. 5 D 0. 9 D 35 = 31.
5 D Low (bid = $22; profit = $2 0. 9 D 80 = 72 D 0. 1 D 80 = 8 D 0. 9 D 30 = 27 D 0. 1 D 30 = 3 D 0. 1 D 2 = 0.
2 D 0. 9 D 2 = 1. 8 D E+ should not expand its capacity so that it can serve 100% of the market. This will have drastic consequences on the nature of the strategic game in that bidding Low becomes PowerTeam’s dominant strategy, and a Nash equilibrium will result in PowerTeam – Low and E+ – High.
This is shown in the table below and results in a profit of 8 times Demand for E+, which is lower than the desired Medium/Medium profit of 15 times Demand. PowerTeam High Med Low E+ High 0. 5 D 80 = 40 D 0. 5 D 80 = 40 D 0. 1 D 80 = 8 D 0. 9 D 80 = 72 D 0.
1 D 80 = 8 D 0. 9 D 80 = 72 D Med 1 D 80 = 80 D 0 D 80 = 0 0. 5 D 30 = 15 D 0. 5 D 30 = 15 D 0.
1 D 30 = 3 D 0. 9 D 30 = 27 D Low 1 D 80 = 80 D 0 D 80 = 0 1 D 30 = 30 D 0 D 30 = 0 00 4) What strategy could E+ use to create cooperation? With no communication in a repeat game, PowerTeam and E+ could utilize the Dead Trigger and Tit for Tat strategies. Dead trigger sets an agreed upon level. If the price falls below that level, punishment (low choice) is chosen thereafter. With the Tit for Tat strategy, each player plays the move the competitor played the previous game.
Neither method is optimal because any misinterpretation or miscommunication will cause each to be stuck in a low profit segment forever. Additionally, these are not credible punishments because neither company would want to have zero profit forever. If the two teams can communicate, which is the case since PJM posts the resultant bids each day, the best cooperation choice is the optimal trigger. Each company would agree to play high. If one company played medium or low, the other company would play low for one period. By cheating a company makes 32 times D more than it would have by cooperating (72 D versus 40 D).
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In the next period, when the other company plays low, the cheating company’s maximum payoff would be 8 times D (assuming it played high); thus it makes 32 times D less in that period than it would have under cooperation (40 D versus 8 D).
Since the net effect of cheating is zero, this would be a deterrent from cheating.
