*Image creds: SMBC*

Here are 18 game theory-related ideas I came up with in the last Game Theory lecture of term. These are things that I think would be interesting to explore and are suited to (but do not require) people who have elementary knowledge of game theory.

- Look into
**Quantum game theory**. - Create a game theory problems tree.
- E.g. choose P -> Bertrand. Don’t choose p -> Cournot.

- Are there any uses for k-price auctions, where k > 2?
**Model marketing material publication times**as congestion or as a game.- When (in what use cases) do you want to find Nash Equilibria (NE) in a short period of time (e.g. in real time)?
- Since ‘efficient NE-finding algorithms’ don’t exist, we want to find
**proxies of NE (or other ‘good’ ideas of equilibria) that are easier to compute**.

- Since ‘efficient NE-finding algorithms’ don’t exist, we want to find
- What is the time needed for players to converge to a Nash Equilibria? (Game and NE-specific, analogous to Markov Chain absorption time).
- Where could we use these results?

- What if people had
**different beliefs**(perhaps because of misinformation)? How could we model games then?- We could model specific types of misinformation, e.g. cases where everyone plays their worst response.

- What about cases where the game setup evolves depending on people’s beliefs?
- (Empirical) When do people most often not playing Nash equilibria? (Particularly interesting in situations where there exists quasi-perfect information.)
- What equilibrium concepts exist that don’t rely on players having correct beliefs?
- Do we have
**axioms for desirable properties in games**as we do with social choice rules?- If so, are there
**theorems analogous to Arrow’s Impossibility Theorem concerning equilibria**?

- If so, are there
- Look up the
**Tragedy of the Anti-commons**. - I imagine that as computational power increases, if Nash Equilibria are roughly predictive or optimal, outcomes of decision-making will converge toward Nash Equilibria faster and more frequently as decision-making is more informed by computation.
- This kind of assumes that people can model the environment reasonably accurately or that everyone shares beliefs, both of which are untrue. But we may still get results in of that sort.
- People may deliberately choose different strategies to persuade people into switching to a different Nash Equilibrium.
- Interesting.

- How do people choose models for payoffs or loss functions in games? (See also reference dependence and loss aversion.)
- Model Nash Equilibria with perturbations. But this is just picking out stable Nash equilibria, right?
**Deduce people’s strategies**based on empirical information using maximum likelihood estimators.- Model Cournot with sunk costs.
- Investigate costs that evolve with the number of players in a game. This is applicable in
**games of R&D, e.g. patents**.