本文探讨了博弈论中的“最后通牒博弈”，它提供了一个简单而强大的框架来理解人类行为和策略。通过分析该博弈，文章揭示了人们对公平的内在偏好，以及在不同情境下（如使用虚拟筹码或真实货币）策略的变化。文章还探讨了在实际生活中，例如自由职业者谈判中，如何应用和理解这种博弈。最后，文章强调了“最后通牒博弈”在揭示人们真正需求和动机方面的价值，并将其推荐为理解战略理性和人类公平之间相互作用的理想案例。

🤝 **博弈设定：**“最后通牒博弈”涉及两个玩家，其中一个玩家提出分配10美元的方案，另一个玩家可以选择接受或拒绝。如果接受，则按照方案分配；如果拒绝，则双方都得不到任何东西。

⚖️ **公平偏好：**研究表明，人类具有对公平的先天偏见。在“最后通牒博弈”中，玩家通常会拒绝不公平的分配，即使这意味着他们什么也得不到。这反映了人们对公平待遇的期望。

💰 **不同情境下的策略变化：**当使用虚拟筹码时，玩家更关注相对收益；而当涉及真实货币时，绝对价值也会影响玩家的决策。这意味着在现实生活中，人们在金钱上的考量会更加复杂。

🎬 **现实应用：**文章通过自由职业电影制作人的案例，说明了“最后通牒博弈”在实际谈判中的应用。在小行业中，建立关系和维护和谐的工作环境也会影响最终的决策，这反映了迭代博弈的动态。

🎯 **核心价值：**“最后通牒博弈”揭示了人们的真实需求和动机，是研究战略理性和人类公平之间相互作用的理想案例。

Published on July 3, 2025 7:05 PM GMT

This mini-post is part of a series looking for alternatives to the Prisoner’s Dilemma when introducing game theory. It summarises and links to the many posts where we’ve used this simple game already.

In this game, you are given $10. To keep the money, you have to give a portion of this $10 away to another player. If we take the contained, rational and self-interested assumptions of game theory, the dominant strategy is simple: give the other player as little as possible. The catch is, if the other player rejects your offer, you both get nothing. This is the Ultimatum Game, a form of take-it-or-leave-it bargaining.

Rearing its Head

The Ultimatum Game is a powerfully simple game theory scenario because it introduces a number of key concepts. This is why it has appeared in numerous posts at nonzerosum.games.

When exploring Negative Moral Licensing, we looked at studies that used The Ultimatum Game to understand human perceptions of injustice. The studies found that humans have an innate bias towards equitable treatment (for good evolutionary reasons).

In Relative Gains—how not to measure success, we asked what happens when the Ultimatum Game is played with counters, or real money, to draw attention to the nature of different payoffs. Because fairness generally concerns relative value (between the players), it stands to reason that player two would reject anything less than an equal share, because to accept less is essentially to lose the game, but when real money is involved, absolute value comes into play (in that the money has real value outside of the relative relationship between players) and so player two might be willing to take a smaller offer to gain real money.In Jaiveer Singh’s Subgame Purrrfection the Ultimatum Game is used as an example of an extensive form game to illustrate subgame perfect Nash Equilibrium. Jaiveer explores how the game conflicts with commonly held norms around fairness and, like with the Prisoner’s Dilemma, finds that these conflicts are mitigated with the introduction of iterated games.

Real Life

As a freelancer filmmaker, I deal with take-it-or-leave-it bargaining every few months. I’ll state my fee and if a producer accepts then I’ll take the job, if not, I won’t. But in a small industry, often I’ll take a lower offer to build a relationship with someone I enjoy working with, so the dynamics of iterated games come into play. Flexibility and acknowledgment of externalities (future jobs, a harmonious working environment) become (rational) factors—but don’t tell my clients this!

So…

Ultimatum games are prevalent in our lives because, no matter how you slice it, every negotiation comes down to a final offer. It’s where things get real, and so our behaviour when faced with such an ultimatum reveals a lot about what we really want, and what motivates us. If you’ve been following our quest for a new poster-child of game theory—one that captures the interplay of strategic rationality and human fairness-you can’t go past the Ultimatum Game.

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Originally published at https://nonzerosum.games.

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