ix-game

To compute Nash equilibria for strategic interactions, this Skill enumerates equilibria, analyzes dominant strategies, and identifies stable outcomes for rational agents in competitive scenarios. It handles both pure and mixed strategy profiles.

Yes, you can calculate the Shapley value for cooperative games to ensure fair allocations. This Skill computes Shapley values, Banzhaf power indices, and core membership to analyze cooperative scenarios and distribute payoffs fairly among agents.

The best way to design a bidding strategy for an auction is to model various auction types including first-price, second-price, English, Dutch, and all-pay formats. This Skill analyzes bidding scenarios to compute optimal strategies for competitive auctions.

Evolutionary dynamics in large-population games work by modeling replicator dynamics and detecting Evolutionarily Stable Strategies (ESS). This Skill analyzes Hawk-Dove and Rock-Paper-Scissors games, plus mean field logit equilibria for large-scale interactions.

Yes, this supports mechanism design by implementing VCG mechanisms and computing Myerson optimal reserve prices. It allows you to design strategic mechanisms that achieve desired outcomes and compute fair allocations in cooperative scenarios.

You should not use game theory analysis when agents behave irrationally or when payoff structures cannot be quantified. This Skill assumes rational agents and requires defined payoff matrices or utility functions to compute equilibria and design mechanisms accurately.