Explain the concept of these questions

There are two players in a simultaneous contest game. Each player i exerts an effort level of e; ( [0, co). Player 1 wins the contest with probability e1 e1 + e2 and Player 2 becomes the winner with the remaining probability. If both players exert zero effort, each would have 50% chance of winning the contest. The winner gets 205, while the loser gets nothing. Exerting one unit of effort has a cost of 1$. Assume further that this game will be repeated infinitely many times. Future payoffs are discounted by a common discount factor of = 0.8 for each player . Find an equilibrium in the form of a grim-trigger strategy. Show and explain your work! Hint: A contest game is a rent-seeking model in which exerting effort is inefficient.1 (i) Alice and Bob participate in a first-price sealed-bid auction, by bidding fa and Lb respectively, where a and b are integers satisfying 0 1 times and both players knew that the game is being repeated exactly n times, how would they play it? Justify your answer. (4 marks) (b) Describe a Nash equilibrium of this repeated game which results in payoffs of -1/(1 - p) for both players. Justify your answer. (2 marks) (c) Is Alice always playing II and Bob always playing B a Nash equilib rium of the repeated game? (2 marks) (d) Find a range of values for p for which there is a Nash Equilibrium (A, B) whose payoff for both players is the same as their payoff if they always played the strategy profile (II, B), and describe A and B. Justify your answers. (8 marks) (ii) The Republic of Alice and the Kingdom of Bob share a polluted river. If the river gets decontaminated, both get a benefit of f4 billion. Alice and Bob will decide simultaneously and independently whether to go ahead with their decontamination projects, and once these are started they cannot be stopped. The cost of decontamination for Alice is f2 billion. The cost of decontamination for Bob is either fl billion or 23 billion: Bob knows this cost but Alice only knows that Bob's cost is fl billion with probability p