# A recap of notation used in this course

• $$\mathbb{R}_{\geq 0}$$: used to denote the set of non-negative reals.
• $$N$$: used to denote number of players and/or number of individuals in a population game.
• $$S_i$$: set of strategies available to player $$i$$.
• $$u_i:S_i\to \mathbb{R}$$: utility function for player $$i$$.
• $$m,n$$: used to denote number of strategies.
• $$r_i,c_i$$: used to denote elements of $$S_1$$ and $$S_2$$ in normal form games with $$N=2$$.
• $$\Delta S_i$$: the set of mixed strategies of player $$i$$.
• $$\sigma_i$$: used to denote an element of $$\Delta S_i$$.
• $$x,y$$: used to denote an unkown in a mixed strategy or states in a stochastic game.
• $$s^*$$: used to denote a best response in a normal form game.
• $$UD_i$$: used to denote the set of undominated strategies in a normal form game.
• $$B_i$$: used to denote the set of strategies that are a best response to some strategy.
• $$\tau$$: used to denote a strategy profile.
• $$\tilde s$$: used to denote a nash strategy in a normal form game.
• $$\mathcal{S}(s)$$: used to denote the support of a mixed strategy $$\sigma$$.
• $$T$$: used to denote the total number of periods for a repeated game.
• $$t$$: used to denote the particular repetition in a series of repeated games.
• $$U_i$$: used to denote the utility to player $$i$$ in a repeated game.
• $$\chi$$: used to denote the population vector in a population game.
• $$u(s,\chi)$$: used to denote the utility of playing $$s$$ in a population $$\chi$$.
• $$\epsilon$$: used to denote proportion of entry population.
• $$\chi_{\epsilon}$$: used to denote the post entry population.
• $$X$$: used to denote the set of states for a stochastic game.
• $$S_i(x)$$: used to denote the set of strategies available to player $$i$$ in state $$x\in X$$ in a stochastic game.
• $$u(i,x,\tau)$$: used to denote the utility to player $$i$$ in state $$x$$ given that the strategy profile is $$\tau$$.
• $$\pi(x’|x,\tau)$$: used to denote the probability of transferring from $$x$$ to $$x’$$ given the strategy profile $$\tau$$.
• $$\lambda$$: used to denote the payoff vector for a cooperative game.
• $$\pi$$: used to denote a permutation.
• $$S_{\pi}$$: used to denote the set of predecessors of $$i$$.
• $$\phi(G)$$: used to denote the Shapley value of a cooperative game $$G$$.
• $$s_i,t_i$$: used to denote the sources and sinks of commodity $$i$$.
• $$\mathcal{P}_i$$: used to denote the set of paths available to commodity $$i$$.
• $$f^*$$: used to denote an optimal flow in a routing game.
• $$\tilde f$$: used to denote a Nash flow in a routing game.