This module continues the discussion of mixed strategies, focusing on their definition and importance in finding equilibria within games. We will analyze the payoffs associated with mixed strategies and explore their application in a tennis game context. The goal is to understand how mixed strategies can serve as best responses and lead to equilibrium outcomes.
In this module, we lay the groundwork for understanding Game Theory by playing engaging games. Students will learn about players, strategies, and payoffs, discovering the importance of pre-defined goals in decision-making. We explore the concept of the prisoners' dilemma and discuss real-world instances of this dilemma along with potential remedies. Additionally, we highlight the significance of different payoffs in coordination problems, emphasizing the need for strategic thinking.
This module delves into the formal ingredients of a game, emphasizing the players, their strategies, and the associated payoffs. We revisit the lessons of avoiding dominated strategies and understanding others' perspectives while analyzing historical scenarios, such as defending the Roman Empire against Hannibal. The iterative deletion of dominated strategies is introduced, leading to a discussion on the difference between something being known and commonly known.
In this module, we apply the concept of iterative deletion of dominated strategies to political elections. Students will analyze how candidates choose policy positions and evaluate the effectiveness of this classic model in real-world political processes. Additionally, we will consider how to enhance this model for better predictive power regarding electoral outcomes, focusing on the interplay between beliefs and optimal strategies.
This module focuses on the concept of best responses in various contexts, such as soccer and business partnerships. Students will learn to avoid strategies that do not represent the best response to others' beliefs. We analyze penalty kicks in soccer to illustrate this concept and explore how it applies to profit-sharing partnerships. The module culminates with an introduction to Nash Equilibrium as a crucial component of strategic decision-making.
This module formally defines Nash equilibrium and explores its significance in strategic interactions. Students will discover various methods to identify Nash equilibria in different games. Through class investment games, we illustrate the existence of multiple equilibria in social settings, discussing the challenges of coordination and the potential remedies, emphasizing the importance of communication in overcoming coordination problems.
In this module, we further apply the concept of Nash Equilibrium to coordination games like the Battle of the Sexes and analyze the classic Cournot model of competition between firms. We will discuss the challenges of collusion in such settings and compare the welfare consequences of Cournot equilibrium against monopoly and perfect competition, providing insight into market dynamics.
This module explores the Bertrand model of imperfect competition, where firms set prices rather than quantities. We discuss a richer model involving differentiated goods, analyzing how customer distribution along a line affects competition. We also revisit strategic political models, focusing on voter distribution and candidates' entry decisions, illuminating the concepts of equilibrium and political strategy.
This module introduces evolutionary stability in the context of social conventions and aggressive versus passive strategies (Hawk-Dove games). Students will learn how evolutionary populations can be mixed and how to predict behavioral variations across different settings. We also examine cases where no evolutionary stable population exists, using natural examples to illustrate these concepts.
This module continues the discussion of mixed strategies, focusing on their definition and importance in finding equilibria within games. We will analyze the payoffs associated with mixed strategies and explore their application in a tennis game context. The goal is to understand how mixed strategies can serve as best responses and lead to equilibrium outcomes.
This module develops three interpretations of mixed strategies in diverse contexts: sports, anti-terrorism strategies, and tax compliance. We explore how mixed strategies can represent beliefs about opponents' actions, as well as the proportions of individuals employing each pure strategy. The implications of these mixed strategies are analyzed, particularly in tax compliance scenarios and how penalties affect equilibrium outcomes.
In this module, we complete the candidate-voter model by analyzing candidates' positioning in equilibrium, emphasizing that they cannot be too far apart. We also engage with Schelling's location game, revealing how segregation can occur in society despite individual preferences. The module highlights the importance of seemingly irrelevant details in models and explores the concept of randomized strategies.
This module examines the concept of evolutionary stability further, analyzing what kinds of strategies are considered evolutionarily stable. By relating these ideas from biology to economic concepts, students will learn how domination and Nash equilibrium intersect with evolutionary stability, providing a comprehensive view of strategic behavior in both fields.
This module introduces sequential games, focusing on how players make decisions in turn-based scenarios. We analyze a game involving a borrower and a lender, employing backward induction to identify solutions. Key concepts include moral hazard, incentive design, and commitment strategies, such as providing collateral, all aimed at addressing issues related to loan repayment.
This module continues the exploration of backward induction, applying it to quantity competition in the Stackelberg model. We analyze both intuitive and calculus-based approaches, discussing first-mover advantages and the role of information in strategic decisions. We also highlight instances where increased information may inadvertently harm a player's position, challenging common assumptions about timing advantages.
This module discusses Zermelo's theorem and its application to games with perfect information, such as chess. Students will learn about strategies in such games and how to derive Nash equilibria in sequential settings. We will analyze the consistency of certain Nash equilibria with backward induction, highlighting cases where threats may be viewed as credible despite lacking rational justification.
This module investigates the chain-store paradox and how to incorporate reputation into game theory. Students will analyze situations where threats or promises may lack credibility, focusing on players' uncertainties about payoffs and rationality. The latter part of the module involves a duel game, emphasizing timing as a critical strategic factor and applying dominance and backward induction to the analysis.
This module develops a simple bargaining model, starting with the ultimatum game and progressing to alternating offer bargaining. Students will learn about discounting and how it influences offers in bargaining scenarios. The module emphasizes that under certain conditions, an equal split offer is accepted, while also considering how bargaining power can be affected by wealth and other factors.
This module covers games with both simultaneous and sequential components, introducing information sets to represent players' limited knowledge. Students will learn to define imperfect information games and construct normal forms for these scenarios. The module emphasizes the importance of information over time and introduces the refined equilibrium notion of sub-game perfection to address inconsistencies in Nash equilibria.
In this module, we analyze games using the concept of subgame perfect equilibrium (SPE). Students will explore various scenarios, such as trust in decision-making and matchmaking in dating. The module emphasizes the importance of consistent backward induction and reveals how strategic effects can significantly influence competitive choices. By rolling back equilibrium payoffs, students will learn to derive SPE in complex games.
This module explores wars of attrition, examining strategic interactions in scenarios like trench warfare and strikes. Students will analyze how prolonged conflicts can arise even with minimal stakes, attributing these occurrences to rational behavior and other motivations like pride. The module highlights the dynamics of attrition games, discussing equilibria that may lead to rapid resolutions or prolonged struggles.
This module discusses the role of repeated games in fostering cooperation through credible promises and threats. Students will learn about the grim strategy and its effectiveness in sustaining cooperation, provided that the game continues over time. The module explores the balance between punishment severity and relationship stability, applying these concepts to moral hazard issues in outsourcing relationships.
This module investigates cooperation in repeated games, analyzing how the structure of the game can influence behavior. Through practical exercises, such as playing the prisoners' dilemma multiple times, students will discover the unraveling of cooperation due to end-game scenarios. The module also explores strategies for potentially infinite games, considering how to maintain incentives for cooperation even when the end is uncertain.
This module examines asymmetric information through two primary settings: verifiable and unverifiable information. Students will learn how signaling and communication can be influenced by incentives. The module discusses the implications of information unraveling in verifiable settings and explores signaling in unverifiable situations, particularly focusing on how education can serve as a signal for potential employers.
This module analyzes auctions, distinguishing between common and private values. Through class activities, students will experience the winner's curse, learning why the winning bidder tends to overpay. The module covers various auction typesâfirst-price, second-price, and open auctionsâand discusses bidding strategies for each. Finally, we start to explore which auction formats yield higher revenues for the seller.