Notation
| \(N\) |
Set of players, \(N = \{1, 2, \dots, n\}\)
|
| \(A_i\) |
Action set of player \(i\)
|
| \(A = \prod_i A_i\) |
Joint action space |
| \(a_{-i}\) |
Action profile of all players except \(i\)
|
| \(u_i : A \to \mathbb{R}\) |
Payoff (utility) function of player \(i\)
|
| \(\sigma_i \in \Delta(A_i)\) |
Mixed strategy of player \(i\)
|
| $^* $ |
Nash equilibrium profile |
| \(v(S)\) |
Characteristic function of coalition \(S\) in cooperative games |
| \(\phi_i(v)\) |
Shapley value of player \(i\)
|
| \(\pi\) |
Policy in reinforcement learning |
| \(Q(s,a)\) |
Action–value function |
| \(\gamma\) |
Discount factor |
| \(\mathbb{E}[\cdot]\) |
Expectation |
Common abbreviations
| BR |
Best response |
| BNE |
Bayesian Nash equilibrium |
| CFR |
Counterfactual regret minimisation |
| ESS |
Evolutionarily stable strategy |
| MARL |
Multi-agent reinforcement learning |
| MDP |
Markov decision process |
| MSNE |
Mixed-strategy Nash equilibrium |
| NE |
Nash equilibrium |
| PD |
Prisoner’s dilemma |
| RL |
Reinforcement learning |
| SPE |
Subgame-perfect equilibrium |
| TU / NTU |
Transferable / non-transferable utility |
| VCG |
Vickrey–Clarke–Groves mechanism |
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