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The Monotonicity Puzzle - BuR - Business Research

The Monotonicity Puzzle - BuR - Business Research

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BuR -- Business Research Official Open Access Journal of VHB Verband der Hochschullehrer für Betriebswirtschaft e.V. Volume 3 | Issue 1 | May 10 | 8--35 Figure 1: Game trees for the contracts NE L NE H W Contract N E L EH 0.60 1.20 0.60 1.20 1.20 1.80 1.20 1.80 0.60 1.20 0.60 1.20 1.20 1.80 1.20 1.80 0.90 3.40 0.45 2.95 1.30 3.00 0.85 2.55 0.45 2.95 0.00 2.50 0.85 2.55 0.40 2.10 The upper row contains payoffs for the first mover; the lower row the payoffs for the second mover. NE L (a) Contract N (non--monotone) NE H W Contract M E L EH 0.60 1.60 0.60 1.60 1.20 1.40 1.20 1.40 0.60 1.60 0.60 1.60 1.20 1.40 1.20 1.40 0.90 3.00 0.45 2.55 1.30 3.40 0.85 2.95 0.45 2.55 0.00 2.10 0.85 2.95 0.40 2.50 The upper row contains payoffs for the first mover; the lower row the payoffs for the second mover. (b) Contract M (monotone) 13

contract M. BuR -- Business Research Official Open Access Journal of VHB Verband der Hochschullehrer für Betriebswirtschaft e.V. Volume 3 | Issue 1 | May 10 | 8--35 Table 3: Contract M. Expected net payoffs to agent in stage 2 given stage-1 decisions expected payoff incomenode no effort effort maximizing action NEL 1.383 1.143 no effort NEH 2.014 1.900 no effort EL 1.395 1.407 (effort) EH 2.047 2.143 effort Again, expected net payoffs can be used to determine the agent’s income-maximizing strategy in stage 1. Since the expected payoff when choosing ‘no effort’ (1.64) at this stage is lower than the expected payoff when choosing ‘effort’ (2.00), the income-maximizing strategy is to choose ‘effort’. That is, income-maximizing agents under contract M also choose ‘effort’ in stage 1 and ‘effort’ in stage 2. If an agent selects ‘no effort’ in stage 1 instead and reaches decision node NEL or NEH, respectively, it is payoff-maximizing to select ‘no effort’ in stage 2 as well. 2.2 Principals’ payoffs To predict principals’ choices, one can easily verify that no contract dominates the other in terms of first-order stochastic dominance or second-order stochastic dominance for any effort strategy selected by agents. Given the decisions of incomemaximizing agents, the expected payoffs for principals selecting contract N is e 1.56 and for principals selecting contract M is e 1.35. (The principal’s decrease in expected surplus of e 0.21 associated with choosing M instead of N is exactly the increase of the agent’s expected surplus of e 0.21.) 3 Experimental design We test five different treatments of the sequential principal-agent game with ten decision rounds each. The basic set-up is as follows: The first mover (principal) has to choose between two similar, incentive compatible contracts N and M. Contract N is characterized by the pay structure given in (7)-(10), whereas (11)-(14) characterizes M’s pay structure. That is, contract N awards the highest payoff to the output sequence {low, high} and contract M does so to the sequence {high, high}. The 14 contract choice determines the payoff for both the first mover and the second mover (agent) for every possible output sequence. The second mover’s effort decision influences the probabilities of the different possible output sequences. In order to get enough observations for agents’ behavior in stage 2, we applied the strategy method when asking for agents’ effort decision at this stage. That is, agents had to state their effort decision for each of the two possible outcomes that could result in stage 1. Table 4 summarizes treatments and sample sizes. Our first treatment is labeled ‘no framing with selected contract information’ (NFS) and serves as our baseline treatment. In NFS, an agent is matched with the same principal in all ten rounds. The principal decides on a contract once and for all rounds and the agent receives information only on the contract chosen by the principal, i.e. agents are given a game-tree visualization of that contract containing probabilities of success and respective payoffs for both players (see Figures 1(a) and 1(b)). The agent must accept the contract offered. ‘No framing’ means that subjects do not receive explicit information on the (non-)monotonicity property of the contract. In these respects, the treatment NFS is comparable to the ’framing principal’ treatment employed by Lukas (2007a) in which framing refers to labeling a principal an ’employer’ who selects a contract (a feature which is also used in our design); but in our treatment parameters were chosen in a way that the non-monotonicity is more explicit (i.e., in contract N), which increases practical relevance of results. Our controlled variations of the baseline treatment allow us to investigate the influence of different features that are not only relevant to the labor-market context, but that could also help to reduce the complexity of the experimental situation. As such, the results might explain the differences between the experimental data obtained in Lukas (2007a) and the empirically observed predominance of monotone contracts. The second treatment (‘framing with selected contract information’, FS) differs from the first one only in that additional information about the contract type is given to the participants, i.e. contracts are explicitly framed as either ‘monotone’ or ‘non-monotone’, respectively. The framing also includes information about the agent’s net payoffs for outcome sequences (x L , x H ) and (x H , x H ) based on the respective effort choices. Principals receive this information for both contracts, while

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