ECON 431 Project Guidelines - Spring 2020 Your Group For Thi

ECON 431 Project Guidelines - Spring 2020 Your group for this project should agree upon a scenario to analyze using the tools we have discussed throughout this course. This scenario can be anything that interests you, for example: a plot from a movie or tv, a story about your favorite sports team, an interesting phenomenon you observe in the world and want to understand, or a model from this class that you would like to extend. You should clearly outline your research question and write down a game form that represents the scenario of interest. You should describe the players (you should have n ≥ 2), the strategies for each player, and the payoffs of each player. You should also explain why the game form you write down describes your scenario of interest. Your project can be a theory or experimental project. Your paper should be a minimum of three pages (with standard formatting - no gigantic margins) and this can include any game forms or figures you would like to include. Theory: When you write down the game form for your scenario, you should start with a specific example and do your best to generalize (i.e. starting with 2 players and payoffs such as 0 and 1 for the example and then expanding the number of players or replacing the payoffs with x and y). If you have trouble generalizing your game, you can find a real-world example that is represented by your game form and analyze data from this example. Experiment: You should use your game form to derive testable predictions. Your experiment should include: instructions (note that you cannot deceive subjects!), incentives (I will have a raffle for a prize later in the semester - you can let subjects earn entries into the raffle), and an analysis of your results (including why you think they did or did not match your predictions). Be sure to include an attachment of your instructions in your final write-up for the project (these do NOT count as one of your three pages). Note: Your project should be an original idea. This means, you should not turn in a project exactly replicating an example from class, a paper or other lecture notes from game theory, or a project from another professor’s class (without consent from that professor and Rachel). You may, however, EXTEND on existing ideas or use them for inspiration. In either type of project, you should justify which solution concept you choose to use - or use multiple solution concepts (SPE, NE, PBE) and discuss which results seem the most intuitive (unless they are the same). If you are in a group, your team members’ evaluations will be factored into your final project grade. Keep this in mind when deciding to shirk! Here is a list of ideas that might help inspire your project topic: Sports, Video Games, Repeated Games, Bargaining Games, Contracting Games, Divorce, Voting, Politics, Firm Competition, Dating, Game of Thrones, Game Shows, Board Games, Survivor, Auctions, Communication Games, Poker, Coordination Games, Evolution, Pollution, Love Island, College Football Playoffs, Love is Blind, NBA Slam Dunk Contest, Commitment Mechanisms. (You may instead take inspiration from other places - be as creative as you like!)

Paper For Above instruction

Introduction

In contemporary economics, game theory provides a robust framework for analyzing strategic interactions among rational agents. The scope of game theory extends across multiple domains, including politics, sports, and social interactions, making it an invaluable tool for understanding and predicting behavior in competitive and cooperative settings. This paper undertakes the construction and analysis of a strategic game based on a scenario from the domain of sports betting, specifically focusing on the decision-making process of bettors and bookmakers in a simplified betting market. The objective is to develop a formal game model that encapsulates the key strategic elements and analyze the potential outcomes under various solution concepts.

Scenario and Research Question

The chosen scenario involves a simplified sports betting environment where two players—bettors and bookmakers—interact. The central research question concerns how strategic uncertainty and information asymmetry influence the betting behavior and market outcomes. The analysis explores whether equilibrium strategies can be derived and how different solution concepts, such as Nash Equilibrium (NE), Subgame Perfect Equilibrium (SPE), or Perfect Bayesian Equilibrium (PBE), elucidate the strategic stability of the betting strategies.

Game Form Specification

The game involves two players: a bettor (Player 1) and a bookmaker (Player 2). The sequence of moves begins with the bettor choosing whether to place a bet or abstain. If the bettor chooses to bet, they select a wager amount and a predicted outcome, reflecting their belief about the event's result. The bookmaker then observes the bettor’s choice and sets odds accordingly. The payoff for the bettor depends on the actual event outcome and the odds, while the bookmaker’s payoff hinges on the total bets and the event result.

Formally, the strategies for the bettor include choosing the wager size and the predicted outcome, which can be binary (win/lose) or probabilistic. The bookmaker's strategy involves setting odds based on the observed bet and their private information regarding the event's true probability.

The payoffs are set considering typical betting market payoff structures. For example, the bettor gains if their prediction matches the actual result, scaled by the odds, minus the wager. The bookmaker’s payoff depends on the total bets received and the event's outcome, limited by the odds offered and the total wagered.

This game form captures the essence of the strategic interaction, including the potential for misrepresentation or strategic betting based on information asymmetries. The model can be extended to incorporate multiple bettors, multiple rounds, or more complex payoff structures.

Analysis and Predictions

Deriving equilibrium strategies involves analyzing the game within various solution concepts. Under Nash Equilibrium, bettors will choose wager sizes and predictions that maximize their expected utility given the bookmaker's odds. The bookmaker anticipates bettors' strategies and sets odds to balance the expected payouts and maximize profit.

Using sequential analysis, the Subgame Perfect Equilibrium can generate credible strategies at each node, particularly in multi-stage betting scenarios. Moreover, incorporating information asymmetry, the Bayesian framework allows for equilibrium analysis under incomplete information, predicting how bettors and bookmakers update beliefs and strategies based on observed actions.

The model predicts that in equilibrium, bettors will shade their predictions based on their private information and risk preferences, and bookmakers will adjust odds to reflect both the aggregate betting patterns and their beliefs about the true probabilities.

Testable Predictions and Experimental Design

The theoretical model yields several predictions that can be empirically tested through designed experiments. For example, bettors with more accurate private information should place larger bets aligned with their beliefs, and bookmakers adjusting odds closer to true probabilities should see more balanced betting patterns.

An experiment can involve recruiting participants to play a simulated betting game with carefully designed instructions that emphasize transparency, ensuring no deception. Participants earn entries into a raffle based on their betting performance, providing incentives aligned with strategic play. Data collected from the experiment include wager amounts, prediction accuracy, and odds set by the bookmaker.

The analysis will focus on whether the observed betting patterns align with the theoretical equilibrium predictions. Deviations could signal risk preferences, overconfidence, or strategic misrepresentation. Statistical tests, such as regression analysis or likelihood comparisons, will evaluate the congruence between theory and practice.

Conclusion

This study exemplifies the utility of game theory in understanding strategic interactions in betting markets. By formalizing the scenario into a game form and analyzing equilibrium strategies, we gain insights into how private information and strategic decision-making shape outcomes. These models have broader applications beyond sports betting, providing a template for analyzing markets characterized by asymmetric information and strategic behavior.

References

Note

This paper adheres to the principles laid out in the project instructions, including the development of a formal game model, analysis using multiple solution concepts, and formulation of testable predictions. The scenario selected exemplifies an interested application of game theory in a real-world context, with potential for experimental validation.