Game Theory, Rubinstein Model, Collective Bargaining and Grexit

“We didn’t want a strike. We want a solution as soon as possible.”

-Jose Luis Rodriguez Salazar, secretary-general of the Independent Union of Volkswagen Workers

Ariel Rubinstein is an Israeli economist who has done lot of work in area of Game Theory esp. its application in area of bargaining. In 1982, he published “Perfect equilibrium in a bargaining model” in which he outlined a model of bargaining called as Rubinstein bargaining model.

'Lots of give and take in that negotiation...they took and we gave.'

The model consists of two players, who during game keep making alternating offers. It describes two-person bargaining as an extensive game with perfect information in which the players alternate offers. The first player makes an offer in the first period, if the second player rejects, the game moves to the second period in which the second player makes an offer, if the first rejects, the game moves to the third period, and so forth. The game goes on till one player accepts an offer. Though in theory they can make unlimited offers, but with round of offer, the allocable surplus goes down. With each round there is delay and delay is cost to players ex. delay will result in loss of sales, production, wages etc. So each player is keen to end negotiations as soon as possible. If game goes on for too many rounds, both sides will end up getting nothing, as at some stage all surplus will get wiped out.



A good example of this game is collective bargaining between management and unions.


In 2001 at Volkswagen plant at Puebla in Mexico, the auto workers went on strike, demanding 30% hike in salary. VW responded with 7% hike. Workers did not agree and strike continued. Workers were losing daily wages while strike was costing VW $ 30 million per day.

In next round, workers demand came down to 19% while VW offered an 8.5 percent pay increase, plus a 1 percent hike for school supplies, and 0.7 percent raise for the basic food basket for workers and their families.

Unfortunately, no agreement could be reached and strike continued, with delay resulting in losses to both sides.


Finally, strike ended with both sides signing an agreement. As per agreement, workers got 10.2 percent hike in wages and additional benefits like coupons for food and children’s school supplies.


“If we use a Rubinstein  bargaining approach, with Greece and the Troika making alternative offers and deciding to accept or reject, the answer depends how patient are the two sides. It turns out that each side’s gets a larger share of the pie the more ‘patient’ he is and the more ‘impatient’ is his opponent. One can make a lower offer to an impatient opponent. “

-Paolo Manasse, Professor of Economics, University of Bologna       

This model can also be applied to international politics. In case of Greece, the public refused to go with reforms suggested by banks and European Union. But Greece with its fragile economy will find it difficult to survive if they move out of Union. European Union too wants Greece to stay within Union. But delay in reaching agreement is costing each side a lot. So as per Rubinstein model chances are both sides will reach some kind of agreement before time runs out.



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