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. 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. 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. 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 (www.ercot.com)
Electricity Market (http://en.wikipedia.org/wiki/Electricity_market)
PJM Interconnection (www.pjm.com)
