Games View of Decisions

Game Theory

The study and theories for strategic interactions are often called "game theory". This approach divides a decision making problem into possible choices that you can make. These are matched by decisions that your opponent or other players make. Your strategies may "pure", in that you always make the same decision, or they might be "mixed" in that you randomly choose one strategy or the other. Similarly, the payout from each interaction may be a pre-determined number or you may only know a probability of a particular outcome. In this introduction to game theory, we will only use "pure" games in which you select from a list of strategies. The first approach will be where you play the game against another player who has the same set of choices that you do. In the second example, we will modify the game to play "against nature", in which the outcomes are determined by the strategy that you choose and what will happen under different environmental scenarios.

Simple game set up

The simplest game is when you have two choices, your opponent has the same two choices and you each have to commit to a strategy without knowing what the other is doing. An example of this set up is given in Table 1. In this example, you might rather not wearing the shirt than to look like a copycat. The values for the possible outcomes would determine what you would choose.

Table 1. A simple game for what to wear to the party. Your choices are limited to the choices in the first column. Your friend chooses independent of you. The outcome of your coolness is given in the table.

	Your friend - wears the same shirt	Your friend - doesn't wear the shirt
You - wear your favorite shirt	You both look like copycats	You look cool, he doesn't
You - don't wear your favorite shirt	He looks cool, you don't	Neither of you look cool or dorky

In the shirt example, if you choose not to wear your shirt, this is an example of a "maximin" strategy. You are choosing to limit your negative outcome by choosing the strategy that gives you the best (maximum) of the worst (minimum) scenario.

Use of a common pool resource - as a game

Another familiar example of this game is the "Tragedy of the Commons" scenario. The commons is a "common pool resource" in that you have no control over who uses it but anyone who uses it decreases its usefulness to others. You have a choice of grazing your sheep on the commons either early or at the approved time. The generally approved time has been determined when both of you would be able to graze 10 sheep. Your neighbor also has the same choices. You have no control of what your neighbor does and you don't know what they will do. The strategies and outcome matrix is given in Table 2.

Table 2: The tragedy of the commons expressed as a pure strategy game. The outcomes for each player are expressed both by rank and with values; best =11, good =10, poor=0,and worst = -1. Early grazing gets you more money but wrecks the pasture.

	Your neighbor - grazes early	Your neighbor - grazes at approved time
You - graze early	You both do poorly.	Best for you, worst for neighbor
You - graze at approved time	Worst for you, best for neighbor	Good for both of you

The game outcomes show that if you cooperate with the approved time, you could very likely have the worst outcome, especially since this is the best option for your neighbor. If you choose to defect from the rules and graze early, the worst possible outcome is "poor" rather than "worst", and there is a chance you can have your "best" outcome. Your most rational choice is the maximin strategy, which is to graze early.

This game illustrates the dilemma of cooperation in the commons in a different way than simply listing the utilities. It shows that if you both choose the maximin strategy, you will both have suboptimal outcomes.

The obvious solution is to agree to cooperate. However, if you are allowed the option to talk to your neighbor and reach an agreement then that is a different game for two reasons. Rather than these being a trivial or picky points, they are actually a very important condition to understand. The first reason is that, in a common pool resource such as this pasture, you don't control who comes in and when they graze. If you and your neighbor agree, there is nothing to keep the other neighbor to just graze there early. As long as it is a common pool resource, you always have the possibility that there is another "neighbor" who can show up unannounced. The second point is that even if you made an agreement with your neighbor over the fence, there are no rules that state what you would do if he broke the agreement. You could agree to cooperate, then he could graze early and guarantee the best outcome for himself.

Some commons are governed by rules that account for monitoring compliance and penalties for infractions. These rules need to be enforceable at a reasonable price otherwise it defeats the purpose of sharing the commons anyway. In contrast to the impression in many of the environmental science texts, the tragedy of the commons is not unavoidable. There are many societies that govern common fisheries, pastures, woodlots and water rights very effectively. Before we jump to conclusions about the inevitability of sub-optimal outcomes in governing common pool resources or that all common pool resources need to be converted into private properties, we should understand how to establish and tend for institutions that favor cooperation.

Playing the game against nature and the "Precautionary Principle"

Using the same type of outcomes matrix, we can define a set of choices for you and a set of outcomes that depend on factors out of human control. This is called a game against nature. This framework is very valuable even if you don't know the risk (or probabilities) associated with each of the possible natural events. Table 3 shows a simple game against nature.

Table 3. Strategies for dealing with a possible tornado. You don't know the probability that a tornado will touch down on your street.

	No tornado	Tornado comes right down your street
You - spend money to prepare for a bad tornado	You "wasted" your money	You suffered only minor damage and lived through the storm
You - spend the money on a new TV	You didn't waste your money and you have a cool TV in front of your lounger	Your house is wrecked and it isn't the same watching your TV from a folding chair

There is no accounting for what some people might do, but the rational choice in this situation is to take the maximin strategy and avoid the costly damage. In environmental science, this is called the "Precautionary Principle". The principle is that if you don't know the probability of the outcomes, you should try to use a strategy that minimized the maximum potential harm. This principle is applied to our use of pesticides and other environmental interventions.

We are playing a similar game against nature when we respond to the threat of global warming and climate change. We can identify several strategies that we could take and we can estimate the potential outcome for different warming scenarios. The structure of the game and the favored strategy is similar to Table 3, take the strategy that avoids the worst possible outcome.

Table 4. Global warming as a game and using the Precautionary Principle, i.e. maximin strategy.

	Turns out, no global warming	Global warming hits hard
You - spend money to prepare for global warming	You "wasted" your money	You suffered only minor damage
You - spend the money on more highways	You didn't waste your money and now you have cool highways	Your life is wrecked and you need all the highways in NY are under water

Although the outcomes above are a bit facetious, the point is that if you take precautions in the face of uncertainty, there is that possibility that this money will be wasted. The opportunity for our society now is to look at this game and change the rules such that we invest in infrastructure and environmental protections that we want anyway, but that will protect or mitigate the effects of climate change.

Summary

The "games" framework is very useful for evaluating different strategies and making decisions. Two examples of how this framework is related to classic environmental problems are presented; the tragedy of the commons and the precautionary principle. Both of these simple games rely on the player choosing the strategy that avoids the worst possible outcome.

References

Coman, Andrew M. 1995. Game theory and its applications in the social and biological sciences. 2nd Edition. Butterworth/Heinmann Publishers.

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