Assumptions

Definition

Assumptions are the foundational beliefs or premises that underlie a model or theory, acting as starting points for analysis. In the context of multiple equilibria and equilibrium selection, assumptions help to clarify the conditions under which different outcomes may arise, shaping the behavior of players in strategic situations. They influence how we interpret results and understand the stability and viability of various equilibria in games.

5 Must Know Facts For Your Next Test

1. Assumptions about player rationality are crucial in determining how equilibria are reached and selected in game scenarios.
2. Different sets of assumptions can lead to multiple equilibria, creating challenges in predicting which equilibrium will actually occur.
3. Assumptions about information availability (complete vs. incomplete information) can significantly affect equilibrium selection and outcomes.
4. Equilibrium selection may depend on additional assumptions regarding risk preferences, payoff structures, and the strategic environment.
5. When assumptions are relaxed or altered, the stability of equilibria can change, potentially leading to entirely different strategic outcomes.

Review Questions

• How do assumptions about player rationality impact the identification and selection of equilibria in game theory?
  • Assumptions regarding player rationality are essential because they dictate how players are expected to behave in a given game. When players are assumed to act rationally, it suggests they will seek to maximize their payoffs based on their beliefs about others' actions. This assumption helps identify Nash equilibria since players' best responses hinge on rational decision-making. If these assumptions are relaxed, it could lead to different behavioral patterns that affect equilibrium outcomes.
• Discuss the role of assumptions in establishing conditions for multiple equilibria in games. How do these assumptions influence which equilibrium is selected?
  • Assumptions play a key role in defining the conditions that lead to multiple equilibria by outlining how players interact and make decisions based on their preferences and available information. For instance, if players have similar payoff structures but differing beliefs about others' actions, this can create several potential equilibria. The specific assumptions made—such as whether players have complete or incomplete information—can significantly influence not only the existence of multiple equilibria but also the processes through which one equilibrium might be favored over others.
• Evaluate how altering foundational assumptions can transform equilibrium analysis and its implications in strategic decision-making.
  • Altering foundational assumptions can dramatically change equilibrium analysis by shifting the theoretical framework within which decisions are made. For instance, changing the assumption from complete information to incomplete information alters how players assess risk and strategize. This can lead to different equilibria being deemed more stable or favorable based on new dynamics introduced by these adjustments. As a result, such changes not only impact theoretical predictions but also real-world applications where strategic decision-making relies on sound models based on initial assumptions.

Related terms

Nash Equilibrium: A situation in a game where no player can benefit by changing their strategy while the other players keep their strategies unchanged.

Mixed Strategy: A strategy in which a player randomizes over different actions, allowing for a probability distribution of choices rather than a single deterministic choice.

Dominant Strategy: A strategy that is optimal for a player regardless of the strategies chosen by other players, leading to a predictable outcome.