Game Theory

This article relates to Game Theory for negotiation.

Source of information TWS

Most negotiations are based on partnership approach but if this is not an option, Game Theory could be a useful tool for difficult negotiations.

Game Theory is a concept where the study of human conflict and cooperation within a competitive situation. In some respects, game theory is the science of strategy, or at least the optimal decision-making of independent and competing actors in a strategic setting. The key pioneers of game theory were mathematicians John von Neumann and John Nash, as well as economist Oskar Morgenstern.

The parties interact and choose their actions in view of what the other parties might think and do.

To win at all cost you need to be tough, and you also need a well-defined strategy.

Simple example of Win Lose

In this scenario there are 2 people in a negotiation. There is only one winner, one will take it all and the other will lose everything.

John owes Richard some money. They can’t agree on how much is owed.

John wants to pay the minimum amount. Joe wants the maximum.

In this simple scenario there are only 2 strategies/ options to meet in the middle.

    John’s Options
    Strategy 1 Strategy 2
Richard Options Strategy 1 Pay £6 Pay £5
Strategy 2 Pay £5 Pay £4

John wants the maximum amount of £6 he knows the other person wants to pay the minimum which is £4, most likely they will meet in the middle £5

In real life a negotiation is not that simple. More options are added. In the second example a maximum of £10 is payable. There are 4 strategies.

    John’s Options    
    Strategy 1 Strategy 2 Strategy 3 Strategy 4
Richard Options Strategy 1 Win Lose Lose Win
Strategy 2 Lose Win Win Lose
Strategy 3 Lose Win Win Lose
Strategy 4 Win Lose Lose Win

To win the Game you need to create more options for the opponent and less options for yourself to hone in on what you absolutely want. You do this by getting rid of options that are inferior that add no value.

Richard wants to take control to get the maximum return. He eliminates strategy 3 and 4 and steers the negotiation to strategy 1 & 2

By narrowing down the strategies Richard gains control of the Game. He has 4 chances of winning and 4 chances of losing – 50:50.

If he included all 4 strategies he would have 8 chances of winning and 8 chances of losing, still 50:50 chance but it doubles his risk.

Strategy 3 and 4 can be your concessions- allow yourself the luxury to lose to the other party.  They have some value but not enough to change the Game.

For example, imagine a game between John and Richard. In this simple game, both players can choose strategy A, to receive £10, or strategy B, to lose £10. Logically, both players choose strategy A and receive a payoff of £10. If you revealed Sam’s strategy to Tom and vice versa, you see that no player deviates from the original choice. Knowing the other player’s move means little and doesn’t change either player’s behavior. The outcome A, A represents a Nash Equilibrium.

You should:

Go in to the negotiation with a clear idea of what you want and eliminate inferior options.  In this situation you help the other party believe that they are getting more from the negotiation.

In a negotiation it is better to make the first move. Making the first move allows you to frame the negotiation and establish the parameters.

Most people enter into negotiations because we expect to come to an agreement. Both sides can make promises and threats but generally neither party wants to walk away with nothing. In general people are willing to be co-operative as long as they get something in return.

What happens if one party has the stronger hand?

For arguments sake in the new scenario, John has a stronger hand. Strategy he thinks he has to pay the other party £100. If he opts for strategy 2 he only has to pay £50. Richard has no bargaining chips and if he fails to reach an agreement he walk away with nothing.

John doesn’t know that Richard has zero options, therefore he believes due to his negotiation powers, he has steered the negotiations towards strategy 2. John has walked away with giving away less than half of what he wanted, a saving of £50. Richard on the other hand had nothing to lose and gains £50.

If John had done more research and preparation he would know that Richard was bluffing and had a weak hand.

Establishing Trust

In a negotiation we all want to win. However if you make a make a commitment to concede and this is valuable to the o

ther party, you have gained credibility but limited your options. This creates trust that progress is being made.

Game Theory and the example of Prisoner’s Dilemma

Two suspects who are business partners are being interrogated.

If they both co-operate they will get a smaller sentence, if one defects he will walk away for free and the other will get a long and harsh sentence.

In this scenario we want to ensure that the other party is not going to defect and leave us in a worse position. Both parties will get a good deal if they agree to work in collaboration they will suffer minimum loss but if one party breaks his promise this creates a win lost situation.

In order to try and get agreement both parties need to try and establish the following:

  • Trust
  • Copying and mirroring. You reciprocate your opponent’s last move.
  • Continuity, if the parties need each other in the future, they are less likely to cheat, or ruin the relationship long term.

Key points to remember

  • Make the first offer
  • Beware of precedence unless it’s for your advantage. Just because something was done before, it doesn’t mean you should accept it.
  • If you make a commitment stick with it. If you make a threat go through with it. Credibility is the key to negotiation, if you lack credibility you lose power.

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