How can you navigate uncertainty in game theory?

1 Understand the types of games

Game theory classifies games into different types based on the characteristics of the players, the information available, and the outcomes. For instance, cooperative games allow players to communicate and form binding agreements, while non-cooperative games require independent and self-interested actions. Simultaneous games involve players making their choices at the same time, without knowing what the others are doing, while in sequential games, players move in a predetermined order and can observe the previous moves. Zero-sum games have a constant total payoff, meaning one player's gain is another's loss; conversely, in non-zero-sum games, the total payoff can vary and players can have mutual gains or losses. Lastly, symmetric games have the same strategies and payoffs for all players, whereas asymmetric games have different strategies and payoffs. By understanding the type of game you are facing, you can apply suitable tools and methods to analyze and solve it.

2 Use decision trees and matrices

Decision trees and matrices are graphical tools that can help you represent and visualize the structure of a game, the possible actions and outcomes, and the payoffs and probabilities. They can also help you identify and eliminate dominated strategies, which are those that always yield a lower payoff than another strategy, regardless of what the other players do. For example, in a prisoner's dilemma game, where two suspects have to decide whether to confess or remain silent, confessing is a dominated strategy for both players, because they would both be better off if they remained silent.

Decision trees are useful for sequential games, where you can trace the branches from the initial node to the final nodes, and apply backward induction to find the optimal strategy for each player. Backward induction is a method of reasoning backward from the end of the game to the beginning, and choosing the best action at each node, given the expected actions of the other players.

Matrices are useful for simultaneous games, where you can display the strategies and payoffs of each player in a table, and use the concept of Nash equilibrium to find the optimal strategy for each player. A Nash equilibrium is a situation where no player can improve their payoff by changing their strategy, given the strategies of the other players.

3 Incorporate uncertainty into your models

Uncertainty can affect your game theory models in various ways, such as not knowing the exact payoffs or probabilities of each outcome, the preferences or beliefs of the other players, or the number or identity of the players. To incorporate this uncertainty, you can use expected utility to measure the satisfaction or value that a player derives from a certain outcome. Bayesian games are also useful for dealing with incomplete information, while stochastic games are useful for considering randomness in the state of the game. In all cases, you can compare the expected utilities of different strategies and choose the one that maximizes your expected utility. Additionally, Bayes' rule can be used to update beliefs based on new evidence, and you must consider expected value and variance when dealing with randomness.

4 Explore different scenarios and strategies

One of the benefits of game theory is that it allows you to explore different scenarios and strategies, and how they affect the outcomes and payoffs of the game. By doing so, you can gain insights into the behavior and incentives of the other players, and anticipate their reactions and responses. You can also test your assumptions and hypotheses, and see how robust and sensitive your models are to changes in the parameters or the environment. For example, you can vary the payoffs or probabilities of each outcome, the number or type of players, or the rules or constraints of the game, and observe how they affect the equilibrium and the optimal strategies.

Exploring different scenarios and strategies can also help you identify and exploit opportunities for cooperation, coordination, or negotiation with the other players, and improve your outcomes and payoffs. For example, you can use signaling, commitment, or reputation to convey your intentions or preferences to the other players, and influence their expectations or actions. You can also use bargaining, coalitions, or contracts to reach agreements or solutions that are mutually beneficial or fair.

5 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?