Game Theory 101: Dominant Strategy and Choice Conflict

Game theory is choice-theory in economics. We did a basic introduction to game theory by looking at one of the most common introductory games in Game Theory, the Prisoner’s Dilemma, here. In that introduction we briefly touched on dominant, or strong, strategy and non-dominant, or weak strategy. Now we’re continuing our understanding of economic theory by understanding dominant strategies.

Dominant strategy emerges in game theory and economic competition because we look for the so-called Nash Equilibrium. In competition, is there a dominant strategy to pursue that is the same across the board regardless of what the other player, or players, do? To stick with the Prisoner’s Dilemma Case: The offer is: (1) If A and B each betray the other, each of them serves two years in prison, (2) If A betrays B but B remains silent, A will be set free and B will serve three years in prison (and vice versa) (3) If A and B both remain silent, both of them will only serve one year in prison (on the lesser charge).

If Player A confesses, then the dominant strategy for Player B is to confess also. If Player A doesn’t confess, then the dominant strategy for Player B is to confess. Thus, we can see that irrespective of Player A’s choices, Player B should always confess. It is always beneficial to him to confess. If he refuses to confess when Player A confesses, he suffers the maximum penalty. If he refuses to confess even when Player A also refuses to confess, he still suffers a penalty while confessing would have gotten him to go free.

In our introduction to Game Theory we also noted the paradoxes of Game Theory. It assumes rational self-interest and the anthropology of homo economicus. Yet, if we employ reason we should cooperate. Thus, heterodox game theorists assert that Game Theory shows the myth of rational man and the homo economicus. Why?

It is rationally (taking the anthropology of self-interested homo economicus as our starting point) the best strategy for both players to take the strategy of confessing. In this reality, both players will receive a two-year prison sentence. If both remain silent, then they will serve one-year prison sentences. Do you see the problem?

By following the dominant strategy, both players actually earn a greater penalty than if they followed the cooperative strategy. But the cooperative strategy is the weak strategy, or the non-dominant strategy. Why?

We have no control over what the other player is going to do. It may very well be the case that the other player will remain silent as agreed upon. But if this is the case, then you should confess if you had perfect knowledge that the other player was going to remain silent. Why? Because you will go free. Thus, we return to the dominant strategy of confessing because economic competition is about yourself. Since we do not have perfect knowledge (or perfect information), and have imperfect knowledge (imperfect information), it is always best to follow the dominant strategy even if the other player in following the dominant strategy results in a two-year penalty instead of a one-year penalty. Why? In a game of perfect information, if we know the other player is going to confess, we should confess. If we know the other player is going to stay silent, we should confess. In a game of imperfect information, we should always confess because confessing is the dominant strategy that we control; if the other player confesses we should hedge our bet and confess to protect ourselves and if the other player stays silent we should opt to confess because if the other player stayed silent we received the best outcome. Thus, we see that there is a dominant strategy in perfect knowledge and imperfect knowledge. Ipso facto, the dominant strategy in all cases is to confess.

Heterodox Game Theorists argue that the problem with Game Theory isn’t the idea of the rational consumer, but a more profound anthropological issue that liberal anthropology (based on the self-making self) fails to acknowledge: Fight or Flight, or, competitive preservation. It is rational man that should be our starting point in economics. Rather, it should be the anthropology of competitive conflict. Given this reality, it is “more rational” to understand how we end up following the path of the dominant strategy despite the fact that if both sides pursue the dominant there will be a greater penalty than if both sides pursued the cooperative strategy.

Dominant Strategy in Game Theory is the choice option available for players irrespective of what the other player(s) pursues. As shown in this example, the dominant strategy is always to confess no matter what the other player does. Therefore, we have derived the dominant strategy.

Game Theory and Dominant Strategy is also useful for more than just economics. It is useful to understand the notion of dominant strategy in international relations, politics, and state relations. But this also opens up other issues. Is there a dominant strategy in international relations? What happens when players are playing from different starting points. For instance, one nation might be following a realist school of interpretation in international relations. Another nation might be following a liberal school of interpretation in international relations. Another nation might be following a geopolitical school of interpretation in international relations. You see the problem that emerges here. Nevertheless, the notion of a dominant strategy is important to recognition in the evolving conundrum of choice conflict.

Thus, heterodox game theorists would say the starting point isn’t rational man but choice conflict. Choice conflict is how we should approach game theory, economics, and even international politics.

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