Robustness to Strategic Uncertainty (Replaced by DP 2010-98)

O. Andersson, C. Argenton, J. Weibull

Research output: Working paperDiscussion paperOther research output

Abstract

We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.
Original languageEnglish
Place of PublicationTilburg
PublisherMicroeconomics
Number of pages32
Volume2010-70
Publication statusPublished - 2010

Publication series

NameCentER Discussion Paper
Volume2010-70

Fingerprint

Strategic uncertainty
Robustness
Uncertainty
Nash demand game
Nash equilibrium
Bertrand competition
Probability distribution

Keywords

  • Nash equilibrium
  • refinement
  • strategic uncertainty
  • price competition
  • Bertrand competition
  • bargaining
  • Nash demand game

Cite this

Andersson, O., Argenton, C., & Weibull, J. (2010). Robustness to Strategic Uncertainty (Replaced by DP 2010-98). (CentER Discussion Paper; Vol. 2010-70). Tilburg: Microeconomics.
Andersson, O. ; Argenton, C. ; Weibull, J. / Robustness to Strategic Uncertainty (Replaced by DP 2010-98). Tilburg : Microeconomics, 2010. (CentER Discussion Paper).
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Andersson, O, Argenton, C & Weibull, J 2010 'Robustness to Strategic Uncertainty (Replaced by DP 2010-98)' CentER Discussion Paper, vol. 2010-70, Microeconomics, Tilburg.

Robustness to Strategic Uncertainty (Replaced by DP 2010-98). / Andersson, O.; Argenton, C.; Weibull, J.

Tilburg : Microeconomics, 2010. (CentER Discussion Paper; Vol. 2010-70).

Research output: Working paperDiscussion paperOther research output

TY - UNPB

T1 - Robustness to Strategic Uncertainty (Replaced by DP 2010-98)

AU - Andersson, O.

AU - Argenton, C.

AU - Weibull, J.

N1 - Pagination: 32

PY - 2010

Y1 - 2010

N2 - We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.

AB - We model a player’s uncertainty about other players’ strategy choices as smooth probability distributions over their strategy sets. We call a strategy profile (strictly) robust to strategic uncertainty if it is the limit, as uncertainty vanishes, of some sequence (all sequences) of strategy profiles, in each of which every player’s strategy is optimal under under his or her uncertainty about the others. We derive general properties of such robustness, and apply the definition to Bertrand competition games and the Nash demand game, games that admit infinitely many Nash equilibria. We show that our robustness criterion selects a unique Nash equilibrium in the Bertrand games, and that this agrees with recent experimental findings. For the Nash demand game, we show that the less uncertain party obtains the bigger share.

KW - Nash equilibrium

KW - refinement

KW - strategic uncertainty

KW - price competition

KW - Bertrand competition

KW - bargaining

KW - Nash demand game

M3 - Discussion paper

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T3 - CentER Discussion Paper

BT - Robustness to Strategic Uncertainty (Replaced by DP 2010-98)

PB - Microeconomics

CY - Tilburg

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Andersson O, Argenton C, Weibull J. Robustness to Strategic Uncertainty (Replaced by DP 2010-98). Tilburg: Microeconomics. 2010. (CentER Discussion Paper).