ISMP 2012, Berlin Alan Holland and Barry Optimising the economic e ffi ciency of O’Sullivan monetary incentives for renewable energy Introduction Mechanism investment Design Potential E-Policy Demonstrator Alan Holland and Barry O’Sullivan Application Research Challenges: Cork Constraint Computation Centre Allocation University College Cork Ireland August 22, 2012
Problem Description ISMP 2012, Berlin Alan Holland and Barry Government policy: increase renewable energy production. O’Sullivan Limited budgets. Introduction Mechanism Lack of information regarding willingness of population to Design share costs. Potential E-Policy Instrument to support policy: grant aid. Demonstrator Application Primary challenge: who should get what level of Research Challenges: grant aid. Allocation Secondary challenge: how to split a budget among competing technologies.
Game Theory ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction A formal way to analyze interaction among rational agents Mechanism Design who behave strategically. Potential Economic modelling tool. E-Policy Demonstrator Application People behave in a selfish manner that maximizes their Research own utility. Challenges: Allocation
Game Theory ISMP 2012, Berlin Alan Holland and Barry O’Sullivan A formal way to analyze interaction among rational agents Introduction who behave strategically. Mechanism Economic modelling tool. Design Potential People behave in a selfish manner that maximizes their E-Policy Demonstrator own utility. Application Solution concept: Nash equilibrium Research Challenges: Allocation Outcome is stable (no agent has an incentive to unilaterally deviate)
Inverse Game Theory ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction game of private information Mechanism Design center chooses the payo ff structure Potential agent’s “type” ✓ 2 Θ E-Policy Demonstrator Application outcome o consists of an allocation and payo ff Research o ( ✓ ) = { x ( ✓ ) , p ( ✓ ) } , x 2 X , p 2 P Challenges: Allocation
Designing An Economic Game ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Inverse Game Theory Design Potential Design rules E-Policy Demonstrator selfish actions lead to socially desirable outcome Application Research Challenges: Allocation
Designing An Economic Game ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Design Allocation Scheme Payment Scheme Potential E-Policy Who gets what. Demonstrator What they pay to the Center in Application exchange. Research Challenges: Allocation
Solar Grant Problem ISMP 2012, Berlin Alan Holland and Barry Altruistic central planner. O’Sullivan Finite budget b to subsidize renewable energy micro Introduction generation. Mechanism Design Set of self-interested agents I (seeking subsidies). Potential Private information held by agent i 1 E-Policy Demonstrator Application Common knowledge: price to acquire and install r Research Pitch of roof p i Challenges: Allocation Orientation o i Latitude l i Value of cashflow stream v i 1 Smart phone applications available for this purpose (e.g. Pitch Gauge).
h p ,o,l,v i ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Design Potential E-Policy Demonstrator Application Research Challenges: Allocation Figure: Roof pitch.
h p, o ,l,v i ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Design Potential E-Policy Demonstrator Application Research Challenges: Allocation Figure: Orientation.
h p,o, l ,v i ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Design Potential E-Policy Demonstrator Application Research Challenges: Allocation Figure: Latitude
Smart Phone: h p , o , l ,v i ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Design Potential E-Policy Demonstrator Application Research Challenges: Allocation Figure: Data Capture
Cost ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Design Potential E-Policy Demonstrator Application Research Challenges: Allocation Figure: Maximum Cost an agent is willing to pay
Goal of Center ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Minimize maximum cost for any agent Mechanism Design Incentivise truthful revelation of private data Potential Allocate grants to those best placed to generate solar E-Policy Demonstrator Application energy cost e ff ectively Research Respect budgetary constraints. Challenges: Allocation
Problem and Rationale ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Makespan minimization problem ( Q || C max ) Mechanism NP-complete Design Potential allocate device acquisition and hosting responsibility (jobs) E-Policy Demonstrator across houses (machines) Application private cost associated with acceptance of that job. Research Challenges: inconvenience is bounded as tightly as possible. Allocation
Greedy Allocation Algorithm ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction 1 order the devices from most expensive to cheapest Mechanism Design 2 Greedily assign each to the household that minimizes the Potential max cost imposition. E-Policy Demonstrator Application 3 A 2-approximation that is non-monotone . Research 4 Leads to strategic manipulability Challenges: Allocation
Non-monotone Allocation Failure Example ISMP 2012, Berlin Alan Holland and Barry 3 devices { d 1 , d 2 , d 3 } and 2 house-owners { h 1 , h 2 } O’Sullivan power of each device: � 1 =10W, � 2 = � 3 = 9 + ✏ W. Introduction Mechanism price for each device: $60 (common to all). Design Each house-owner has private value of $5 / W and Potential E-Policy (5 � ✏ )$ / W, resp. Demonstrator Application greedy algorithm d 1 ! h 1 , d 2 ! h 2 and d 3 ! h 3 Research Challenges: Cost c 1 = 60 � (10 ⇥ 5) = $50, Allocation c 2 = 2 ⇥ (60 � (45 � 4 ✏ � ✏ 2 )) ⇡ $30. Note: if v 2 increases to 5 + ✏ , he loses the second device.
Solution ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Complete search to ensure optimality Design Intractable: potentially large problem instances Potential E-Policy Demonstrator Compromise: approximation scheme with guarantees of Application monotonicity. Research Challenges: Allocation
Approach: Monotone Algorithm ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism 1 Random 3-approximation [Kovacs 2005] Design 2 Randomized rounding of partial allocations Potential E-Policy Demonstrator 3 Implementable within a truthful mechanism (critical Application payment scheme). Research Challenges: Allocation
Payment Scheme ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Critical payments Design Potential The minimum cost declaration to be awarded that item. E-Policy Demonstrator Implementable within a truthful mechanism. Application Research Challenges: Allocation
Future Work ISMP 2012, Berlin Alan Holland and Barry O’Sullivan Introduction Mechanism Empirical study of expected outcomes using simulations Design Potential Pilot Subsidy Auction E-Policy Demonstrator Emilia Romagna region of Italy Application Research Challenges: Allocation
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