From my doctoral course
This note comes from the doctoral course “Game Theory and Bargaining”. I rewrote the explanations in my own words and recomputed the numerical examples.
What is bargaining?
In bargaining two (or more) parties can reach a shared surplus by agreeing, but they disagree on how to divide it (the price of a house, a wage, the division of labour in a family, the terms of an international contract). Each side knows an agreement is better than a failed negotiation but wants a larger share. The question is: what determines how much each gets?
Power factors
- Patience (impatience): the one who worries less about the passing of time can wait longer and therefore gets more. (Example: in a strike the cost of waiting is not the same for employer and worker; whichever is hurt less is stronger.) The mathematics is in Nash’s solution and Rubinstein’s model.
- Risk of breakdown: if each offer may, with some probability, break the whole negotiation, the one who fears breakdown less gets more.
- Outside options (the disagreement point): if I can have an acceptable position without this negotiation (another buyer, another job, the possibility of divorce), my power is greater. This is the BATNA (best alternative to a negotiated agreement) in Position-based and principled negotiation. A subtle point: an outside option has an effect only when it is “credible” and better than the negotiated share; if it is worse than the share I get from negotiating, threatening to leave for it is ineffective.
- Credible commitment: someone who “locks” themselves into a position (a contract, reputation, an irreversible cost) forces the other to accept, provided it is credible. Example, the game of chicken: if one throws the steering wheel out where the other can see, their chance of winning rises.
- Asymmetric information: if only one side knows its true value, it has an incentive to lie (for example “the firm says it is weak”); the other must infer from behaviour, and the cost of waiting (delay) can be a signal of information. That is why countries sometimes go to war though agreement would have been better overall. (Bayesian games and signaling)
- Credibility of words: a threat or promise whose execution hurts the speaker is not credible and has no value (see the “empty threat” in Ultimatum, Stackelberg and sequential games).
My reading
I think the most important thing this topic shows is that bargaining power is almost never a “right”; it is structure: the cost of waiting, outside options and information. So to negotiate better, change the structure before the meeting (build an outside option, reduce the cost of waiting, gather information) and not just talk loudly.
Related: Nash’s solution and Rubinstein’s model.