Research map / Multi-agent systems and games / Games and equilibria
Is Knowledge Power? On the (Im)possibility of Learning from Strategic Interactions
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Shows via a meta-game PNE analysis of repeated Bayesian games that an informed player achieves her Stackelberg value while an uninformed player can be blocked from hers, and that with mutual partial information the informativeness ordering does not determine who wins.
Problem
Whether an a-priori uninformed player can learn through repeated strategic interactions alone to attain her optimal Stackelberg value, when players choose learning algorithms as actions in a meta-game and have asymmetric information about the game.
Approach
Models repeated Bayesian games as a meta-game whose actions are learning algorithms (with signals of given precision) and studies pure Nash equilibria; shows that with one fully informed player, any informational gap persists (the less-informed player can be blocked from her Stackelberg value in some games), while with both partially informed the more-informed player is not necessarily the one who
Key results
- If P1 is fully informed, for every prior D there is a PNE of the meta-game where P1 achieves StackVal_1(G) up to o_T(1) average utility via a Stackelberg-strategy plus no-swap-regret construction.
- For every threshold p* < 1 there exists a game family and prior D such that no PNE of the meta-game gives the partially informed P2 her expected Stackelberg value StackVal_2(D), with a gap of Omega_T(1).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Give P1 perfect knowledge of the realized game while P2 has an imperfect signal | Repeated-game meta-game at PNE · Every game family and prior D | P1 expected average utility | Helped |
| Leave P2 partially informed while P1 knows the realized game | Repeated-game meta-game at PNE · Constructed prior D, p_2≤p^star<1 | P2 expected average utility | Hurt |
| Make both players partially informed rather than having a fully informed player | Repeated-game meta-game at PNE · Constructed D for each player and p_1,p_2<1 | expected average utility relative to Stackelberg value | Mixed |
| Provide P2 with independent external signals that successfully learn the realized game | P2 in the repeated-game meta-game · Every D for which P2 can successfully learn independently | P2 expected average utility | Helped |
| Allow learning from repeated interactions instead of independent external signals | P2 in the repeated-game meta-game · Constructed prior D | P2 average Stackelberg value | Hurt |
Surprising findings
- Learning the game through repeated interactions can succeed in a PNE while the player still fails to attain her Stackelberg value, so the obstacle is applying learned knowledge rather than learning itself.
- When both players are partially informed, the more-informed player does not necessarily win: the less-informed player can learn the game faster due to the structure of the prior.
Limitations
- Results are information-theoretic and assume computationally unbounded players.
- Assumes signals are costless and truthful, with nature not strategically designing them.
- Analysis focuses on pure Nash equilibria of the meta-game in the T-to-infinity limit.
Experimental setup
Builds on: no-swap-regret learning Stackelberg games repeated games with incomplete information (Aumann and Maschler) meta-game of learning algorithms
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