How can you overcome limitations when applying game theory in real-world situations?

1 Identify the relevant players

One of the first steps in applying game theory is to identify the relevant players and their preferences, payoffs, and strategies. However, this can be difficult in complex and dynamic situations, where there may be hidden or unknown players, incomplete or asymmetric information, or changing preferences and payoffs over time. To overcome this limitation, you can use methods such as scenario analysis, sensitivity analysis, or Bayesian updating to account for uncertainty and variability in the players and their characteristics. You can also use empirical data, surveys, or experiments to estimate the preferences and payoffs of the players and validate your assumptions.

2 Choose the appropriate model

Another challenge in applying game theory is to choose the appropriate model that captures the essence of the situation and the behavior of the players. There are many types of game models, such as simultaneous or sequential, cooperative or non-cooperative, zero-sum or non-zero-sum, repeated or one-shot, and so on. Each model has its own assumptions, implications, and limitations, and may not fit every situation. To overcome this limitation, you can compare different models and evaluate their strengths and weaknesses, using criteria such as realism, simplicity, tractability, and predictive power. You can also use hybrid models or extensions that incorporate features such as bounded rationality, learning, signaling, or reputation.

3 Find the equilibrium solution

A key concept in game theory is the equilibrium solution, which is a set of strategies for each player that is mutually best response, meaning that no player can benefit by deviating from their strategy given the strategies of the others. However, finding the equilibrium solution can be challenging, as there may be multiple, none, or mixed equilibria, depending on the model and the parameters. To overcome this limitation, you can use algorithms, such as backward induction, iterated elimination of dominated strategies, or best response dynamics, to find the equilibrium solution or eliminate non-equilibrium outcomes. You can also use concepts such as Nash equilibrium, subgame perfect equilibrium, or Pareto efficiency to select among multiple or mixed equilibria.

4 Analyze the outcomes and implications

Once you have found the equilibrium solution, you can analyze the outcomes and implications of the game for each player and for the social welfare. However, this can be challenging, as there may be trade-offs, conflicts, or paradoxes that arise from the game, such as the prisoner's dilemma, the tragedy of the commons, or the Braess paradox. To overcome this limitation, you can use tools such as payoff matrices, decision trees, or game diagrams to visualize and compare the outcomes and implications of the game. You can also use concepts such as dominant strategies, dominant coalitions, or core solutions to identify the optimal or stable outcomes and implications of the game.

5 Evaluate the robustness and applicability

The final step in applying game theory is to evaluate the robustness and applicability of your game-theoretic analysis and solution. However, this can be challenging, as there may be limitations, caveats, or biases that affect the validity and reliability of your game-theoretic reasoning and decision making. To overcome this limitation, you can use methods such as robustness checks, counterfactual analysis, or experimental testing to assess the sensitivity and generalizability of your game-theoretic analysis and solution. You can also use concepts such as equilibrium refinements, evolutionary stability, or mechanism design to improve the robustness and applicability of your game-theoretic analysis and solution.

6 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?