Approximating large games

One of the big lessons of market design is that market participants may have big strategy sets.  This means that analyzing naturally occurring strategic settings may exceed our ability to model and analyze them as fully specified games.

Here's a paper that explores an interesting, somewhat related idea:

Christian Kroer, Alexander Peysakhovich, Eric Sodomka, Nicolas E. Stier-Moses (2021) Computing Large Market Equilibria Using Abstractions. Operations Research, Articles in Advance 01 Oct 2021, https://doi.org/10.1287/opre.2021.2163

"Abstract. Computing market equilibria is an important practical problem for market design, for example, in fair division of items. However, computing equilibria requires large amounts of information (typically the valuation of every buyer for every item) and computing power. We consider ameliorating these issues by applying a method used for solving complex games: constructing a coarsened abstraction of a given market, solving for the equilibrium in the abstraction, and lifting the prices and allocations back to the original market. We show how to bound important quantities such as regret, envy, Nash social welfare, Pareto optimality, and maximin share/proportionality when the abstracted prices and allocations are used in place of the real equilibrium. We then study two abstraction methods of interest for practitioners: (1) filling in unknown valuations using techniques from matrix completion and (2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market. We find that in real data allocations/prices that are relatively close to equilibria can be computed from even very coarse abstractions."