Optimisation and game theory · Maths EE idea · Solid

Cooperation in the repeated prisoner's dilemma

A research question to start from

Under what conditions on the discount factor can cooperation be sustained in a repeated prisoner's dilemma?

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Why it works as a maths EE

A precise threshold derived from geometric series and compared across strategies.

Mathematics you would need

Payoff matrices
Geometric series and discounting
Strategies such as tit-for-tat and grim trigger
Inequalities

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

Analyse the one-shot game.
Derive the threshold for grim trigger.
Compare strategies in a tournament you design and explain the results.

Scope and difficulty

Solid. Solid.

Pitfalls

Tournament without theory.
Discounting unexplained.

Where to start reading

Search a library catalogue or a university's open lecture notes for: repeated prisoner's dilemma discount factor grim trigger condition. 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

Plan this EEOpens the free EE planner with this question as a starting point. Sharpen the questionSix quick checks for a focused research question. Self-check a draftCheck a section against each criterion, free.