This comprehensive roadmap guides you from foundational concepts through cutting-edge research in game theory. The field uniquely combines rigorous mathematics with practical applications across economics, computer science, biology, and social sciences.
Build a tool to analyze 2x2 and 3x3 games. Find all pure strategy Nash equilibria, dominated strategies, and mixed strategy best response correspondences equilibria. Visualize.
Implement a tournament of strategies for iterated Prisoner's Dilemma (Tit-for-Tat, Always Defect, Pavlov, etc.). Analyze which strategies perform best and why.
Create variations of RPS (Rock-Paper-Scissors-Lizard-Spock, weighted payoffs). Compute mixed strategy Nash equilibria. Build a bot that plays optimally.
Implement Nim and analyze winning strategies. Extend to other combinatorial games (Chomp, Hex). Use backward induction to find optimal play.
Simulate first-price, second-price, and all-pay auctions. Compare revenue and efficiency across auction formats. Analyze bidding strategies for different valuations.
Create a simulation of the public goods game with varying contribution levels and free-riding. Visualize how cooperation evolves with different parameters.
Implement Battle of the Sexes and Stag Hunt games. Create interactive visualizations showing multiple equilibria and coordination problems.
Build a bot for simplified poker (Kuhn poker or Leduc Hold'em). Implement CFR algorithm to find approximate Nash equilibrium strategies. Visualize strategy profiles.
Analyze infinitely repeated games with different discount factors. Compute the set of feasible and individually rational payoffs. Verify folk theorem conditions.
Implement multiple voting systems (plurality, Borda count, approval, ranked-choice). Analyze strategic manipulation and Condorcet paradoxes with simulated elections.
Implement Gale-Shapley algorithm for stable matching. Simulate college admissions or residency matching. Analyze incentive compatibility and strategic misrepresentation.
Model strategic network formation where players choose connections. Analyze stable networks under different cost-benefit structures. Visualize network evolution.
Simulate traffic routing as a congestion game. Compute user equilibrium vs. social optimum. Calculate price of anarchy for different network topologies.
Create a tool for designing simple mechanisms (single-item auctions, public project decisions). Check incentive compatibility and implement VCG payments.
Simulate replicator dynamics for various games (Hawk-Dove, Prisoner's Dilemma). Visualize phase portraits and identify evolutionarily stable strategies.
Build a custom multi-agent environment and train agents using MARL algorithms (IQL, QMIX, MADDPG). Compare convergence to Nash equilibrium vs. other outcomes.
Implement a combinatorial auction for complex allocation problems (spectrum, logistics). Solve winner determination problem. Compare different payment rules.
Analyze separating and pooling equilibria in signaling games (job market, education signaling). Implement perfect Bayesian equilibrium finder for finite types.
Create a limit order book simulation where multiple agents compete. Implement market-making strategies and analyze equilibrium spreads and depth.
Build a platform for analyzing coalition formation in cooperative games. Compute core allocations, Shapley value, and stability concepts for various games.
Implement Rubinstein bargaining and variations. Analyze how discount factors, outside options, and impatience affect equilibrium outcomes.
Model a security domain (airport screening, network defense) as a Stackelberg game. Solve for defender's optimal mixed strategy commitment. Visualize coverage.
Implement various no-regret learning algorithms (Hedge, EXP3, multiplicative weights). Analyze convergence to correlated vs. Nash equilibrium in different game classes.
Implement Deep CFR for large-scale imperfect information games. Apply to custom poker variants or other domains. Compare with tabular CFR and analyze scalability.
Model a large-population game using mean field approximation. Solve using PDE methods or neural networks. Compare with finite-population equilibria.
Use neural networks to design mechanisms for specific objectives. Implement end-to-end differentiable auction learning. Test on allocation problems with complex constraints.
Model blockchain consensus as a game (longest chain, BFT). Analyze incentive compatibility and security under different attack scenarios. Quantify centralization risks.
Implement level-k reasoning and quantal response equilibrium models. Conduct human-subject experiments or agent simulations. Compare predictions with behavior.
Train agents to develop communication protocols emergently. Use neural networks with discrete or continuous communication channels. Analyze evolved languages and compositionality.
Design and implement fair division algorithms for strategic agents (cake cutting, rent division). Prove or test incentive compatibility. Compare efficiency-fairness tradeoffs.
Frame adversarial machine learning as a two-player game. Implement attacks and defenses as strategies. Analyze equilibria and provide robustness certificates.
Build a continuous-time matching market with arrivals and departures. Implement thick market design principles. Optimize for welfare under uncertainty.
Create a network game where agents learn about network structure and payoffs. Implement distributed learning algorithms. Analyze emergence of coordination and information diffusion.
Build a comprehensive framework incorporating multiple behavioral biases (fairness, loss aversion, probability weighting). Predict behavior in various games and validate empirically.
Success Tip: Start with core equilibrium concepts, implement algorithms to solidify understanding, and gradually explore specialized topics aligned with your interests. The field uniquely combines rigorous mathematics with practical applications across economics, computer science, biology, and social sciences.