The Nash equilibrium for calculable results

The John Nash equilibrium explained simply

In corporate practice, it is often desirable to achieve calculable results, even if this is at the expense of possible individual payout efficiency. A stable, risk-avoiding business is even laid down as a basic requirement in corporate governance in many companies. One encounters this security-oriented thinking in many institutional private equity firms.

In negotiation situations, such a constellation is found when none of the other parties has an incentive to deviate from this constellation. In the world of game theory, we have then reached a Nash equilibrium. All “players” reciprocally choose their best response strategy. A Nash equilibrium exists in such a combination of strategies where each participant chooses an option with which the other participants have no incentive to deviate from this combination.

Examples of the John Nash equilibrium

Example “assurance game”: If two cooperation partners commit to a project, they both receive the highest payoff (4, 4). If they are not particularly committed, they both receive only a reduced payout (2, 2). If one of the cooperation partners is fully committed and the other is not, then the one who is not committed receives a high payout, but not the full payout, because he benefits from the contribution of the other, but his contribution is missing in the result; the one who is committed only receives a lower payout on balance because he has taken on the whole burden (3, 1 and 1, 3 respectively). There are two Nash equilibria (4, 4) and (2, 2). If the two cooperation partners trust without a doubt that their partner will commit, they will opt for the payoff-dominant constellation (4, 4) and both fully commit; if this trust is not sufficiently pronounced, they will opt for the Nash equilibrium at the low level (2, 2). If both do not commit, each avoids the risk of having to settle for a minimal payoff. However, if both partners chose to “engage”, they would both do better.

The example shows that the Nash equilibrium is a stable, i.e. calculable solution, although it is not efficient. If there is sufficient trust or if there is an effective sanctioning institution in case of deviation from the “engage” option, the constellation that doubles the payoff for each participant would come into play.

In organisations, suitable framework conditions for low-risk, payout-optimised cooperation can be created by building trust and introducing sanctioning institutions. To this end, it is advisable to ensure that all those involved develop the best possible understanding of the whole, that they get to know each other as personally as possible and that agreed courses of action are also enforced.

It can happen that several Nash equilibria exist and that the challenge is to choose the optimal Nash equilibrium for all those involved. Difficulties usually result from a lack of coordination between the participants.

Example “chicken game”: Two car drivers drive towards each other at full throttle. The one who swerves, the “chicken”, receives two points, the other 4. If neither swerves, each receives one point, and both can assume that they will not survive the collision. If both evade at the same time, each receives 3 points. If the participants want to survive, there are the two Pareto-optimal Nash equilibria that one of the participants evades, with the asymmetric payoff variants (4, 2) or (2, 4). To safely avoid a collision, both drivers would swerve and forgo the possibility of an individual maximum payoff. There is no other way to solve the coordination problem.

The significance of the Nash equilibrium for companies

Individuals and organisational units act with their individual goals under given conditions, producing, intentionally or not, collective (macro) outcomes. Game theorist Andreas Diekmann noted that these macro-results are the result of isolated but often interconnected individual actions at the micro-level (aggregation problem with strategic interdependence). He pointed out that game-theoretic solution concepts, such as the Nash equilibrium, transform individual actions into collective effects. Game theory can thus explain properties of systems on the basis of social interactions.

Besides the Nash equilibrium, the Pareto-optimal equilibrium is also relevant for decision-making situations in practice.

Calculation of the Nash equilibrium

To determine a Nash equilibrium, knowledge of the ranking of preferences is sufficient. Quantitative utility values are not necessary. This makes the determination of Nash equilibria easier in practice.

How to reach the Nash equilibrium

Coordination problems in multiple Nash equilibria, as they occur in the game of chicken, can be solved by social norms and sanctions. Laws, contracts and basic instructions are such rules if it is foreseen that sanctions will come into effect in case of adverse behaviour. These can enable and stabilise cooperation. In addition, rules can help to better structure decision-making situations if violations of the rules are linked to sanctions. In the language of social scientists, such rules are called institutions. Institutions prescribe behaviour; new institutions can even change behaviour. By designing institutions appropriately (mechanism design), behaviour can be influenced in such a way that the results intended by all participants are actually achieved. Institutions can substitute for trust and have a coordinating effect.

Use such institutions in your company to ensure how to proceed in principle in the event of a coordination problem.

Example: An example of this can be found in the form of traffic lights in road traffic, which randomly lead to either a (4, 2) or a (2, 4) payout. When crossing a traffic light-controlled intersection repeatedly, justice prevails and all participants know that they survive.

Example: Institutions commonly used in business practice include pledges, deposits, product liability, bonus systems, patent law and catalogues of fines. All institutions act as permanent and predictable incentive mechanisms for the participants to behave in the mutually agreed manner.


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