Optimisation and game theory · Maths EE idea · Solid
Mixed strategies and Nash equilibria
A research question to start from
How can mixed-strategy Nash equilibria be found in two-player games, and what do they predict in games such as rock–paper–scissors with unequal payoffs?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
An optimisation within probability with clear, checkable answers.
Mathematics you would need
- Payoff matrices
- Expected value
- Indifference conditions
- Linear equations
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Define equilibrium and find pure equilibria.
- Derive mixed equilibria with indifference conditions.
- Analyse a modified game and discuss realism.
Scope and difficulty
Solid. Solid.
Pitfalls
- Economics essay.
- Equilibria found by software only.
Where to start reading
Search a library catalogue or a university's open lecture notes for: mixed strategy Nash equilibrium indifference principle; rock paper scissors unequal payoffs. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).
Make it your EE
Similar ideas
- Cooperation in the repeated prisoner's dilemmaOptimisation & gamesSolid
- Can any voting system be fair?Optimisation & gamesAmbitious
- Cutting a cake fairlyOptimisation & gamesSolid
- Why the simplex method finds the optimumOptimisation & gamesAmbitious
All optimisation and game theory ideas · the full ideas library