Game Theory
Introduction
Game theory is a widely used modeling method for studying. It is a decision-making strategy that incorporates strategic interaction and simulates reality manageably. It is used by biologist, psychologists, economists and management theorists, and political scientist and public policy analyst.
There are 5 types of games:
- Incumbent-Rival game
- The Defense Game
- The Prisoners Dilemma
- The Slippery Pete and Governor Finagler Game
- The M-V Game
There are also 4 components of the games:
- Preference of players
- Strategies
- Payoffs
- Rules and Beliefs environment
The Incumbent-Rival Games:
This game consists of 2 players, two strategies, a win or lose outcome and an assumption that the incumbency is at an advantage.
In the movie Divergent, Abnegation is in power making them the incumbent. Their known rival was Erudite because this faction believed they should be the ones in power. As we can see from the game tree model below, the only way a rival can win is if the incumbent does not raise funds and the rival does, resulting in Incumbent at 2 and rival at 10. The only reason why Erudite rose was because they chose to raise an army and Incumbent did not.
For this game to be successful for the rival is for them to work backwards, or what is called a backwards induction. The rival would need to look forwards and work their way backwards. For example, by seeing that the only way to win is seeing the end result of (I’2, R’10), rival knows that if Incumbent makes a move to raise funds (or an army), the best choice for them would be to not raise fund (an army) because the result of the tree shows they would lose (I’10, R’2).
The Defense Game
In this game, there are two players, 3 strategies (escalate, deescalate, and status quo), 3 outcomes (hawk, dove, and neutral defense policy), and the game environment is simulation.
Say America (Country U) is having conflicts with China (Country C). To better make this decision, they take a look at the defense game table.
America has to decide between escalating, deescalating, or status quo in this situation. If China decided to Escalate, the best option for America is to status quo policy in military which would result in (A’4, C’2). They would continue to make these decisions until someone wins.
The Nash Equilibrium in this for this would be if both America and China chose defense as it owuld result in (8,8). This shows that both parties are better off, without making their components worse off.
Prisoners Dilemma
This game consists of 2 player (prisoners), 2 strategies (cooperate or lie), payoff between 0 to 5 years of prison time, and belief that strategies and payoffs are known, and moves are simultaneous.
To better explain this game theory, we can use the hit tv series, Suits. in this series, Mike Ross, suspect 1, is accused of being a fraud and would be sent to prison. However, he was given an ultimatum to serve 2 years in prison or turn Harvey in, who is his mentor and suspect 2. Below is the table of what would happen if Harvey and Mike choose to corporate or lie.
If Harvey, suspect 2, chooses to cooperate, the option for Mike that would give him the best result is to also cooperate as 4 is greater than 0. If Harvey chooses to lie, the best option for Mike is to also lie, as 5 is greater than 1.
The Nash Equilibrium is a situation where two or more competitors are better off not changing their existing strategy. It is a law that no one wants to break, even in the absence of police. For this game, it would be if Mike and Harvey both cooperated because no one could be made better off without making someone worse off.
Risk
Say you’re invited to a poker party. You’re told that you have a 5% chance of winning $10,000, otherwise, you walk away with $100. For this kind of money, you have to ask yourself how much you’re willing to pay for the buy in for this gamble? Or your expected utility.
The equation for this is E(u): pu (x) + (1-p) u (y)
The Expected utility for this poker game is $505. This is the most you should want to pay as a buy in for this game.
Say you’re in the game and $5,000 and you are given the choice to go all in with the chance to win the $10,000, but if they lose, they lose everything. Or you can cash out and walk away with the $5,000. If you choose to walk away with the $5,000, you are considered risk averse. A risk averse person is reluctant to take major risk. They would rather walk away with a lower amount, than to risk walking away with nothing at all.
Conclusion
Game theory is a useful tool when deciding the best strategy in competitive situations. It enhances one’s reasoning and decision-making skills in a complex world.