Prisoner's Dilemma Explained in Energy Sector


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Prisoner's Dilemma Explained in Energy Sector

  1. 1. Prisoner’s Dilemma Date: January 5, 2009 Name: Maria Medvedeva
  2. 2. PART I: Game Theory and Prisoner’s Dilemma “Game Theory” is complex but strategically important subject in making economic, political and commercial decisions. It is a study of cooperation and conflict. Long before the “Game Theory” military commanders applied systematic thinking to influence troops’ motivation and enemy decisions. General Cortez conquered Mexico having a very small army. To show Aztecs his willingness to stay as well as to eliminate Spanish troops’ desire to return, he publicly burned their ships. For many years economists have been studying the underlying logic that governs decisions when choosing strategies to maximize payoffs. Prisoner’s Dilemma is a game where two players make a decision of either cooperation or defection by considering actions of the other party. The outcome is to understand the dominant strategy and adjust the game to achieve equilibria (favorable outcome for both). Let us assume that CA and Sun plan to introduce security software in the Middle East. Since market is low in IT maturity, it requires awareness events. These are costly and bring very few leads. Sales occur when customers experience a security breach and call for a fix. There is a possibility that IT Managers purchase the software by attending such event. Each company can chose to either conduct or eliminate it from the marketing strategy. Figure 1 shows payoffs for each situation. One company chooses to conduct the event and attract all potential buyers (payoff 8), whereas the other eliminates this strategy (payoff 0). If both companies run the event, there might be an increase in buyers but advertising costs would decrease net revenues (payoff 3 both). If the event is eliminated, companies would sell based on customer requests (payoff 5 both). SUN CONDUCT ELIMINATE CONDUCT 3, 3 8, 0 CA ELIMINATE 0, 8 5, 5 Figure 1: The Prisoner’s Dilemma Game Since the game is symmetric, no matter what the other party does conducting this event is the best strategy for each company individually. This is where the dilemma of pursuing individual interests arises as eliminating this event would lead to a better financial result for the group.
  3. 3. If economic conditions changed, companies could achieve cooperation in a repeated game. SUN and CA would adopt a trigger strategy called “tit for tat” contingent on the action chosen by the competitor. The experience leads companies to assess consequences and reconsider actions to avoid retaliation. The result is a mutual reciprocity: companies do not seek to maximize individual payoff at the expense of the other. References: Game Theory at Work, James D. Miller
  4. 4. PART II: Prisoner’s Dilemma in Deregulated Electric Market The case of Prisoner’s Dilemma often occurs in the deregulated electric market. United States has thousands of plants ranging in efficiencies (production costs) and capacities. For this example, Gas Power Plants A and B would participate in a Dutch auction by submitting bids for a block of energy to be dispatched. Market demand is low during Off Peak and higher during On Peak hours (Figure 2). While supply stack does not change, the market needs enough generation to fulfill its demand. The requirement for this example is 100 MW from the two plants. The market will select plants to dispatch based on the lowest bid structure. Market Supply and Demand On Peak Demand 49 44 Price ($/MWh) 39 Off Peak Demand 34 29 24 19 200 350 650 750 900 1200 1450 1550 1650 1750 1850 1950 Capacity (MW) Hydro Nuclear Coal Gas/Others Deman Demand Dem Demand d and Figure 2: Market Supply and Demand Curve for Electricity Since MC Hydro < MC Nuclear < MC Coal < MC Gas, gas plants are likely to be dispatched last. Figure 3 describes marginal costs of Gas Plants A and B at various capacity levels. Capacity Idle Capacity MC ($/MWh) (MW) (MW) Min 50- Plant A 45 Max100 20 Min 50- Plant B 40 Max100 30 Figure 3: Plant A and Plant B Marginal Costs The first game (Figure 4) includes a strategic decision for each plant to dispatch or remain idle during Off Peak hours. Submitted bid to the market is equal to production cost = MC x Capacity. Plant B has clearly a dominant strategy as the market will always take the lowest price ($4000).
  5. 5. Plant B DISPATCH IDLE DISPATCH $2250, $2000 $4500, $-1200 Plant A IDLE -$900, $4000 -$900, -$1200 Figure 4: Prisoner’s Dilemma for Power Plants – Off Peak Hours Plant A knows that neither the market is willing to bare the cost nor B is cooperating. Though there might be a Nash Equilibrium, player B will never be satisfied with such payoffs. Plant A has choices to shut down, sell its plant or repeat the game by lowering the bid during Off Peak and increasing during On Peak hours, gradually turning to profitability. In a repeated game (Figure 5) Plant A recalculates the bid since idle capacity is a sunk cost. New MC (min) = 45- (900/50) = 27 $/MWh. Respectively, MC (max) = 45- (900/100) = 36 $/MWh. This time the market would always chose to buy 50MW and 50MW from both plants as the total cost is lowest ($3350). The market forces companies to cooperate and achieve equilibrium. Plant B DISPATCH IDLE DISPATCH $1350, $2000 $3600, $-1200 Plant A IDLE -$900, $4000 -$900, -$1200 Figure 5: Prisoner’s Dilemma for Power Plants – Off Peak (2nd Iteration) To cover the losses incurred during Off Peak hours, Plant A changes its bid for On Peak with new MC (min) = 27+45 = 72 $/MWh and respectively MC (max) = 36+45 =81 $/MWh. As the market demand is high, there is a high chance that high bids from Plant A would be accepted. Plant A will gradually increase its bid to generate profits. This example showed forced cooperation for both companies. The other factors that make cooperation easier include reducing number of players and improvement of technologies. References: ERCOT ISO ( Electricity Market ( PJM Interconnection (