1.
Being an artist and applying to competitions means dealing with rejection.
See also: Tattfoo Tan’s iheartrejectionletters.com.
2.
But dealing often with rejection doesn’t mean accepting everything that comes your way. Artists aren’t powerless. We have agency. When an “opportunity” presents itself, an appropriate reaction is to evaluate benefits and costs.
From “Standard Questions for Artists” from Standard Deviation by Helena Keefe (via ArtPractical.com):
Given an opportunity…
Do I believe in what this institution does/stands for? Is it the ideal venue for this project/my work? Does my work feel alive in this context?…
Does this opportunity help me meet or get to know people I may want to work with in the future? Will it enable conversation with people I want to be in conversation with? Is this opportunity helping me reach the audience I want to reach?…
Is there enough freedom in this opportunity? Would saying no to this opportunity be saying yes to something else I care more about? Is this the best artworld for my work? Is it the most effective use of my time/money/energy?
[I’d even ponder, “Is this what I want to do with my life?”]
…Am I being instrumentalized? Am I okay with that?
Am I happier making my living separate from making my art?
3.
Artists, too, can be selective, and reject things that aren’t good fits for us. Indeed, taking a pass on an opportunity can be a generative, productive action.
From Non-Participation: Call for Submissions by Lauren van Haaften-Schick:
The project, Non-Participation, will be a collection of letters by artists, curators, and other cultural producers, written to decline their participation in events, or with organizations and institutions which they either find suspect or whose actions run counter to their stated missions. These statements are in effect protests against common hypocrisies among cultural organizations, and pose a positive alternative to an equally ubiquitous pressure to perform. At the heart of the project is the notion that what we say “no” to is perhaps more important than what we agree to.
Historic instances and examples include: Adrian Piper’s letter announcing her withdrawal from the show Reconsidering the Object of Art: 1965-1975 at LA MoCA, stating her opposition to Phillip Morris’ funding of the museum and requesting that her criticizing statement be publicly shown; A letter from Jo Baer to a Whitney Museum curator canceling an upcoming exhibition on the grounds that her work was not being taken seriously because she is a woman artist; Marcel Broodthaers open letter to Joseph Beuys questioning the relationship between artists and exhibiting institutions; and, just recently, critic Dave Hickey‘s public announcement of his “quitting” the art world.
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This tactic is oppositional to always saying yes; to the (non-)strategy of waiting for more powerful or influential dealers/curators/critics to “save” artists from obscurity and precarity; and to making art only for external validation. You will risk upsetting people and possibly being seen as “difficult.” But to do otherwise is to run the risk of adopting values—self-interest, opportunism, careerism—not your own, which are harmful to your practice and your fellow artists.
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See also: Art Practical’s current issue, Value/Labor.
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Addendum, added 4/10/2014:

Sarrita Hunn, “How to…Make an (Alternative) Institution” // Source: makethings-happen.christinewongyap.com.
See also: Sarrita Hunn’s “How to… Make an (Alternative) Institution,” a freely downloadable PDF ‘activity sheet’/visual essay for Make Things (Happen). In the third of three steps, Hunn describes “Noncooperation/Radical Non-Participation.” Also online at Temporary Art Review.