# RESOURCE BOUNDED DECISION-THEORETIC BARGAINING WITH FINITE INTERACTIVE EPISTEMOLOGIES

### Paul Varkey, Piotr Gmytrasiewicz

#### Abstract

In this paper, we study the problem of bilateral bargaining under uncertainty. The problem is cast in an interactive decision-theoretic framework, in which the seller and the buyer agents are equipped with the ability to represent and reason with (probabilistic) beliefs about strategically relevant parameters, the other agent’s beliefs, the other agent’s beliefs about the current agent’s beliefs, and so on up to finite levels. The inescapable intractability of solving such models is characterized. We present a realization of the paradigm of (resource) bounded rationality by achieving a trade-off between optimality and efficiency as a function of the discretization resolution of the infinite action space. Memoization is used to further mitigate complexity and is realized here through disk-based caching. In addition, the inevitability of model extinction that arises in such settings is dealt with by indicating an intuitive realization of the absolute continuity condition based on maintaining an ensemble model, for e.g. a random model, that accounts for all actions not already accounted for by other models. Our results clearly demonstrate an operationalizable scheme for devising computationally efficient anytime algorithms on interactive decision-theoretic foundations for modeling (higher-order) epistemic dynamics and sequential decision making in multi agent domains with uncertainty.

#### References

- Aumann, R. and Brandenburger, A. (1995). Epistemic conditions for nash equilibrium. Econometrica, 63(5):1161-1180.
- Cho, I.-K. (1990). Uncertainty and delay in bargaining. Review of Economic Studies, 57(4):575-95.
- Cramton, P. C. (1984). Bargaining with incomplete information: An infinite-horizon model with two-sided uncertainty. Review of Economic Studies, 51(4):579-93.
- Doshi, P. and Gmytrasiewicz, P. (2005). Approximating state estimation in multiagent settings using particle filters. In Proceedings of the Fourth International Joint Conference on Autonomous Agents and Multiagent Systems.
- Fudenberg, D. and Tirole, J. (1983). Sequential bargaining with incomplete information. Review of Economic Studies, 50(2):221-47.
- Gmytrasiewicz, P. and Doshi, P. (2005). A framework for sequential planning in multi-agent settings. Journal of Artificial Intelligence Research, 24:49-79.
- Grossman, S. J. and Perry, M. (1986). Sequential bargaining under asymmetric information. Journal of Economic Theory, 39(1):120-154.
- Harsanyi, J. C. (1968). Games with incomplete information played by 'bayesian' players, i-iii. Management Science, 14:pp. 159-182, 320-334, 486-502.
- Kaelbling, L. P., Littman, M. L., and Cassandra, A. R. (1998). Planning and acting in partially observable stochastic domains. Artificial Intelligence, 101:99- 134.
- Kalai, E. and Lehrer, E. (1993). Rational learning leads to nash equilibrium. Econometrica, 61(5):1019-45.
- Lovejoy, W. (1991). A survey of algorithmic methods for partially observed markov decision processes. Annals of Operations Research, 28:47-65. 10.1007/BF02055574.
- Perry, M. (1986). An example of price formation in bilateral situations: A bargaining model with incomplete information. Econometrica, 54(2):pp. 313-321.
- Rubinstein, A. (1982). Perfect equilibrium in a bargaining model. Econometrica, 50(1):97-109.
- Rubinstein, A. (1985). A bargaining model with incomplete information about time preferences. Econometrica, 53(5):1151-72.
- Sobel, J. and Takahashi, I. (1983). A multistage model of bargaining. Review of Economic Studies, 50(3):411- 426.
- Varkey, P. (2010). Bounded rational decision theoretic bargaining using finite interactive epistemologies (technical report). http://www.cs.uic.edu/~pvarkey.
- Zamir, S. (2008). Bayesian games: Games with incomplete information. Discussion Paper Series dp486, Center for Rationality and Interactive Decision Theory, Hebrew University, Jerusalem.

#### Paper Citation

#### in Harvard Style

Varkey P. and Gmytrasiewicz P. (2011). **RESOURCE BOUNDED DECISION-THEORETIC BARGAINING WITH FINITE INTERACTIVE EPISTEMOLOGIES** . In *Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,* ISBN 978-989-8425-41-6, pages 219-225. DOI: 10.5220/0003176802190225

#### in Bibtex Style

@conference{icaart11,

author={Paul Varkey and Piotr Gmytrasiewicz},

title={RESOURCE BOUNDED DECISION-THEORETIC BARGAINING WITH FINITE INTERACTIVE EPISTEMOLOGIES},

booktitle={Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,},

year={2011},

pages={219-225},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003176802190225},

isbn={978-989-8425-41-6},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the 3rd International Conference on Agents and Artificial Intelligence - Volume 2: ICAART,

TI - RESOURCE BOUNDED DECISION-THEORETIC BARGAINING WITH FINITE INTERACTIVE EPISTEMOLOGIES

SN - 978-989-8425-41-6

AU - Varkey P.

AU - Gmytrasiewicz P.

PY - 2011

SP - 219

EP - 225

DO - 10.5220/0003176802190225