New answers tagged nash-equilibrium
6
There is no guarantee that symmetric games have symmetric equilibria.
See this paper for concrete examples.
There is also no guarantee that symmetric games have pure-strategy equilibria. For example, the following game is symmetric and has no pure-strategy equilibria
$$
\begin{array}{cccc}
& \mathrm{a} & \mathrm{b} & \mathrm{c}\\
\mathrm{a} &...
3
Since the choice of $q_i$ can be conditioned on $(s_i,s_j)$, strategies in this game are of the form $(\hat s_i, \hat q_i(s_i,s_j))$. For the given values $\alpha=3$ and $k=1$, the SPNE can be calculated as the profile where $s^*_i=1/3$ and $q^*_i\equiv 1$. Indeed, production levels $q_i^*=1$ are the unique NE in all subgames, independently of the chosen $...
0
I'll assume that $S$ is a constant. By the way, the solution for the SPNE is $q_i = \frac{k}{\alpha - 2}$ which is derived from $q_i = (q_j + k)/(\alpha - 1) = ((q_i + k)/(\alpha - 1) + k)/(\alpha - 1)$.
To answer your question, one should know what SPNE does. It is actually a refinement of NE by eliminating non-credible threats. Knowing this, the idea ...
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