The Ultimatum Game: When Theory and Reality Diverge

The ultimatum game is one of the best-known examples of how far a game-theoretic solution can deviate from experimental reality. The rules are simple: 10 euros are to be split between two players. One player makes a single offer, and the other can either accept or reject it. If he accepts, the money is divided as proposed — if he rejects, neither player gets anything.

From a game-theoretic standpoint, the solution is unambiguous: to maximise his own share, the proposer offers as little as possible — in whole euros, that means exactly one euro. A fully rational second player accepts, because one euro is better than nothing. In experiments with real people and real money, however, this solution does not hold: agreements are reached on average only at around four euros — still somewhat short of the “fair” 5/5 split, but far removed from the game-theoretic 1/9 solution.

This is exactly where behavioural economics comes in, putting the basic assumptions of game theory to the reality check. It shows that in real life, fairness, reciprocity, image and self-perception also play a role in decisions.

Why Game Theory Remains Indispensable as a Reference

At first glance, this seems to render game theory obsolete: why derive abstract, mathematical solutions to a strategic interaction if they never materialise in reality anyway? Yet declaring it superfluous on those grounds is itself a fallacy. For it is only through a mathematically derived reference solution that the deviations and their causes can be studied at all.

What is more, the game-theoretic solution remains a solution within the realm of what is theoretically possible. It tells you how far you can go and where you want to end up — and lets you work in a targeted way on resolving the reasons for the deviations. In the ultimatum game, for instance, the results converge towards the game-theoretic solution when the players do not know each other, never meet again, are separated by physical distance, or when the second player is “trained” in that direction over time. Anyone who uses game theory in procurement gains precisely this point of reference: they know how far a negotiation can be pushed.

Asymmetric Information and the ZOPA

In preparing procurement negotiations, too, the game-theoretic reference solution and psychologically anchored behaviour drift apart. These contradictions can be traced back to cognitive biases, to incentive problems, or to both at once. First, though, one thing has to be understood: negotiations — at least in procurement — almost always rest on asymmetric information.

In highly simplified terms, this concerns the location of the “zone of possible agreement” (ZOPA) — that range between the price a buyer is willing to pay at most and the price a seller wants to achieve at minimum. Any price point within this range would be an agreement that benefits both sides and is therefore acceptable. The negotiation decides how the ZOPA is divided up — and each side wants the final agreement to lie as close as possible to the other's limit.

From a procurement perspective, this information asymmetry can be countered by deriving the seller's minimum price through cost calculations. With the right tools and the necessary prior knowledge, this works well — yet even the best calculation never fully dismantles a supplier's informational edge. It is from this circumstance that the following cognitive biases arise, and underlying incentive conflicts can harden them still further. How such situations can be prepared methodically is shown by the work around procurement negotiations.

Cognitive Biases 1 to 3: Leverage, Market Comparisons and Competition

  • Bias 1: Proving high margins is a negotiation lever. A lever — unlike a mere argument — is the genuinely existing ability to influence the negotiating partner's business case. The decision in favour of a competitor is the prime example: with it, procurement dissolves the business case for all other suppliers. Bundling, too, is a lever, because the supplier receives more volume and can recalculate and optimise its overall business case. Merely proving to a supplier that it adds a high profit, or hides it in its costs, by contrast, is not yet a lever — at least not from a game-theoretic point of view. Even with a genuine monopolist it becomes clear that it does not set its optimal price via a fair margin on costs, but via the optimisation of the offered quantity. In practice, a cost calculation can nonetheless have an effect: monopolists rarely admit how comfortable the margin is, and an appeal to fairness or a reminder that the supplier itself once argued via the cost structure can certainly take hold. The bias lies in believing that the calculation alone is already the lever. Game theory teaches us: separate levers and arguments clearly, and channel the preparation effort above all into developing genuine levers.
  • Bias 2: Higher competitor offers justify the incumbent supplier's price. A broad tender is often meant to give a feel for current market prices or to enable a change of supplier — precisely when a single supplier's prices are hard to assess. If the competitors initially come in more expensive, the existing price level suddenly looks appropriate: evidently the others can't do it any cheaper either. But here apples are being compared with pears. On one side, the tailor-made offer of the incumbent supplier, who is already in the business, assesses the order costs most realistically, and whose price is already a negotiated starting point. On the other, competitor offers that price in uncertainties and risks, may not yet have fully understood the precise requirements, and are moreover unnegotiated. Game theory looks at the supplier's pricing — and thereby supports the hypothesis that the direct comparison is not actually complete to begin with.
  • Bias 3: Only suppliers with a realistic chance belong in the negotiation process. At first glance this sounds reasonable — why keep a bidder who can't win the contract anyway? But one has to differentiate. Anyone who is eliminated on technical or substantive grounds — a bidder you couldn't admit even at a cost of zero euros because it doesn't meet the requirements — should be excluded early for reasons of efficiency. Excluding a supplier merely because it probably won't prevail commercially, however, is a classic cognitive bias. For the value of an additional supplier is measured not only by the immediate savings from a switch, but also by its effect on the design options and the intensity of competition in the negotiations.

Cognitive Biases 4 to 6: Fake Gifts, Inflation and Competitive Pressure

  • Bias 4: A supplier that has already conceded 20% has no potential left. Suppliers exploit this bias deliberately during the approach: they name a price and grant a supposedly large discount early on — often with the note that this is now really the final offer, valid only briefly. The hope is that procurement gratefully accepts the 20% and does not negotiate further. If it does negotiate anyway, the supplier doggedly points to the savings already granted and portrays procurement as out of touch with reality or even exploitative. From game theory we know: caution is always called for when one side bestows supposed gifts. The 20% by no means imply that the supplier couldn't go considerably lower still. The royal road is a hard competitive mechanism that neutralises the psychological effects of a bilateral negotiation and denies the supplier such arguments.
  • Bias 5: The new offer is justified once inflation has been priced in correctly. In the inflationary environment of recent years, the question of price drivers gains relevance, especially when renegotiating long-running contracts in which current supplier prices are hard to assess. Suppose one could derive the price drivers correctly: then the old price could be taken as the baseline and rolled forward by the price development. But what if the historical baseline was already too high? In concentrating on price development alone, one must not forget to scrutinise the level of the old prices as well. As so often, here too explicit competitive pressure is the best remedy.
  • Bias 6: Suppliers always know the competitive pressure. This widespread assumption indirectly underscores one's own negotiating competence — after all, a good buyer is regarded as one who consistently emphasises competition as a lever in the supplier relationship. But salespeople have a mind and a perspective of their own: it is part of a good salesperson's job description to highlight the outstanding features of their own product or service. With incumbent suppliers, this can lead to a misjudgement of their own market position. Paradoxically, this ignorance is a psychological — indeed a game-theoretic — advantage in negotiations: pressure, for instance via the announcement of a supplier switch, only works if the other side takes it as true and serious, and the buyer first has to pull that off credibly. Explicit mechanism design achieves this via the so-called indifference condition: with maximum commitment, the process makes it credible that competition exists and that procurement — through the delta valuation in the sense of a TCO perspective — is indifferent between the offers.

From Cognitive Bias to Competitive Mechanism

The six cognitive biases share a common root: they confuse arguments with genuine levers and underestimate the power of a clearly designed competitive mechanism. Game theory supplies the reference solution for this — the point of reference that reveals how far a negotiation can actually carry, and where the psychological effects of a bilateral negotiation begin to work against procurement.

In training and in supporting concrete procurement negotiations, Competitio translates these principles into practice — with over EUR 35 billion in negotiated volume across 16 industries and Prof. Dr. Christian Rieck on its scientific advisory board.

Do you want to systematically eliminate cognitive biases in your negotiations and build genuine levers instead of arguments? Talk to us.