Combinatorial Group Testing with Selfish Agents

We study the Combinatorial Group Testing (CGT) problem in a novel game-theoretic framework, with a solution concept of Adversarial Equilibrium (AE). In this new framework, we have $n$ selfish agents corresponding to the elements of the universe $[n] =\{0,1,\ldots,n-1\}$ and a hidden set $K \subseteq [n]$ of active agents of size $|K| = k \ll n$. In each round of the game, each active agent decides if it is present in a query $Q \subseteq [n]$, and all agents receive feedback on $Q \cap K$. The goal of each active agent is to assure that its id could be learned from the feedback as early as possible. We present a comprehensive set of results in this new game, where we design and analyze adaptive algorithmic strategies of agents which are AE's. In particular, if $k$ is known to the agents, then we design adaptive AE strategies with provably near optimal learning time of $O(k \log(n/k))$. In the case of unknown $k$, we design an adaptive AE strategies with learning time of order $n^k$, and we prove a lower bound of $\Omega(n)$ on the learning time of any such algorithmic strategies. This shows a strong separations between the two models of known and unknown $k$, as well as between the classic CGT, i.e., without selfish agents, and our game theoretic CGT model.