Bayesian-Nash Equilibrium

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Q1. Consider two players, A and B, involved in a gun fight. However, the players have asymmetric information about each other’s ability to shoot. Player A does not know if Player B is a good shooter (type G) or a bad shooter (type B) for sure, but he knows that Player B could be a type G with probability p. Player B is perfectly informed about Player A’s type. Each player can choose to fight or to concede. The payoffs of the players are defined as follows. If player A chooses to concede, he yields ‘0’ pay off irrespective of the other player’s action. If A fights, he yields a payoff of 1 if the opponent concedes; if both players fight, then their payoff is (-1,1) if player B is type G and (1, -1) if player B is type B.

a.Represent this situation as a Bayesian Game (10 marks)

b.Find its Bayesian-Nash Equilibrium if p<1/2 and p>1/2. (15 marks)

Sample Solution

The term Rahn literally means constancy or holding and binding.
Synonymous Terms: Collateral, Pledge, Pawn, Mortgages,

Shariah View

In the Quran, Allah says: If you are on a journey and cannot find a scribe, then use the receipt of pawned object. (Al-Baqarah-283).
In a hadith Anas (r.a) said: “The Holy Prophet (pbuh) pawned a shield with a Jew in Madinah and he took from him some barley for his family.’’

In terms of Equity-based, the presence of rahn is not to secure the capital & or profit, but loss due to negligence.

Rahn as a security means the ownership will remain with the pledgor.

Rahn’ “Benefits to Customers & Islamic Bank vis-à-vis Securing Risk”

Mohd. Johan Lee alluded as regard of the Rahn whereby:

It is an obligation of a debtor to pay the debt even without
any collateral. Thus, having an asset as a collateral even in
the form uncertainty is better than not having one.
The owner of the asset will own all the benefits, usufruct,
income generated or growth of the capital until any events
of default happens.

The specifc nature of Rahn is to provide assurance that a
pledgor shall fullfil the obligation to meet the pledgor’s liability to the pledgee.

Put it Simply, the existing of Collateral could secure uncertainty events such as default risk, breach of contracts, and possibility of inability to pay either deliberately or unintentionally in the future after the financing facility given to the customers. Hence, the stance of both parties secured by the rahn per se.

It important to note:

Since it is as a security, it means there is no Transfer of ownership to the pledgee.
In other words, all benefits and profit which might be generated from
The security would be retained in the hands of the pledgor. Similar to loss situation.

Shariah Maxim: “entitlement to profit depends upon liability for loss”

Rahn’ “Issues, Concerns, Challenges”

Overdependence on the Security Pledged:

It is undeniable fact that the potential risk of NPF either in IFIs could be mitigated by providing a security of consumer’s. However, it should be borne in mind that IB should have awareness as re

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