Honest signaling in zero-sum games is hard, and lying is even harder

TL;DR

This paper demonstrates the computational difficulty of designing optimal signaling schemes in zero-sum games, showing that even approximate solutions are hard to find under standard complexity assumptions, and introduces a new model involving dishonest signaling.

Contribution

It establishes tight quasi-polynomial time bounds for approximate signaling schemes and introduces a novel dishonest signaling model with hardness results.

Findings

Finding an psilon-approximate symmetric signaling scheme requires quasi-polynomial time.

Finding a multiplicative approximation is NP-hard.

Even with a dishonest signaling model, near-optimal schemes are NP-hard to compute.

Abstract

We prove that, assuming the exponential time hypothesis, finding an \epsilon-approximately optimal symmetric signaling scheme in a two-player zero-sum game requires quasi-polynomial time. This is tight by [Cheng et al., FOCS'15] and resolves an open question of [Dughmi, FOCS'14]. We also prove that finding a multiplicative approximation is NP-hard. We also introduce a new model where a dishonest signaler may publicly commit to use one scheme, but post signals according to a different scheme. For this model, we prove that even finding a (1-2^{-n})-approximately optimal scheme is NP-hard.